Skip to main content

2017 | OriginalPaper | Buchkapitel

Special Submanifolds in Hermitian Manifolds

verfasst von : Ion Mihai

Erschienen in: Topics in Modern Differential Geometry

Verlag: Atlantis Press

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The geometry of submanifolds, in particular in Hermitian manifolds, is an important topic of research in Differential Geometry.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat E. Abbena, An example of an almost Kähler manifold which is not Kählerian. Boll. Un. Mat. Ital. 3–A(6), 383–392 (1984)MathSciNetMATH E. Abbena, An example of an almost Kähler manifold which is not Kählerian. Boll. Un. Mat. Ital. 3–A(6), 383–392 (1984)MathSciNetMATH
3.
Zurück zum Zitat D. Blair, Riemannian Geometry of Contact and Symplectic Manifolds (Birkhäuser, Boston, 2002)CrossRefMATH D. Blair, Riemannian Geometry of Contact and Symplectic Manifolds (Birkhäuser, Boston, 2002)CrossRefMATH
5.
Zurück zum Zitat J. Bolton, F. Dillen, J. Fastenakels, L. Vrancken, A best possible inequality for curvature-like tensor fields, Math. Inequalities Appl. 12, 663–681 (2009) J. Bolton, F. Dillen, J. Fastenakels, L. Vrancken, A best possible inequality for curvature-like tensor fields, Math. Inequalities Appl. 12, 663–681 (2009)
6.
Zurück zum Zitat V. Borrelli, B.Y. Chen, J.M. Morvan, Une caractérisation géométrique de la sphère de Whitney, C.R. Acad. Sci. Paris Sér. I Math. 321, 1485–1490 (1995) V. Borrelli, B.Y. Chen, J.M. Morvan, Une caractérisation géométrique de la sphère de Whitney, C.R. Acad. Sci. Paris Sér. I Math. 321, 1485–1490 (1995)
7.
Zurück zum Zitat B.Y. Chen, Geometry of Submanifolds (M. Dekker, New York, 1973)MATH B.Y. Chen, Geometry of Submanifolds (M. Dekker, New York, 1973)MATH
8.
Zurück zum Zitat B.Y. Chen, Geometry of Submanifolds and Its Applications (Science University of Tokyo, Tokyo, 1981)MATH B.Y. Chen, Geometry of Submanifolds and Its Applications (Science University of Tokyo, Tokyo, 1981)MATH
9.
Zurück zum Zitat B.Y. Chen, CR-submanifolds of a Kähler manifold. J. Differ. Geom. 16, 305–323 (1981)MATH B.Y. Chen, CR-submanifolds of a Kähler manifold. J. Differ. Geom. 16, 305–323 (1981)MATH
10.
Zurück zum Zitat B.Y. Chen, Geometry of Slant Submanifolds (Katholieke Universiteit Leuven, Leuven, 1990)MATH B.Y. Chen, Geometry of Slant Submanifolds (Katholieke Universiteit Leuven, Leuven, 1990)MATH
12.
14.
Zurück zum Zitat B.Y. Chen, On Ricci curvature of isotropic and Lagrangian submanifolds in complex space forms. Arch. Math. (Basel) 74, 154–160 (2000)MathSciNetCrossRefMATH B.Y. Chen, On Ricci curvature of isotropic and Lagrangian submanifolds in complex space forms. Arch. Math. (Basel) 74, 154–160 (2000)MathSciNetCrossRefMATH
15.
Zurück zum Zitat B.Y. Chen, Some new obstructions to minimal and Lagrangian submanifolds in complex space forms. Jpn. J. Math. 26, 105–127 (2000) B.Y. Chen, Some new obstructions to minimal and Lagrangian submanifolds in complex space forms. Jpn. J. Math. 26, 105–127 (2000)
16.
17.
Zurück zum Zitat B.Y. Chen, A series of Kählerian invariants and their applications to Kählerian geometry. Beiträge Algebr. Geom. 42, 165–178 (2001)MATH B.Y. Chen, A series of Kählerian invariants and their applications to Kählerian geometry. Beiträge Algebr. Geom. 42, 165–178 (2001)MATH
18.
Zurück zum Zitat B.Y. Chen, \(\delta \)-invariants, inequalities of submanifolds and their applications, Topics in Differential Geometry (Editura Academiei Române, 2008), pp. 29–155 B.Y. Chen, \(\delta \)-invariants, inequalities of submanifolds and their applications, Topics in Differential Geometry (Editura Academiei Române, 2008), pp. 29–155
19.
Zurück zum Zitat B.Y. Chen, Total Mean Curvature and Submanifolds of Finite Type (World Scientific, Singapore, 2015)MATH B.Y. Chen, Total Mean Curvature and Submanifolds of Finite Type (World Scientific, Singapore, 2015)MATH
21.
Zurück zum Zitat P.J. De Smet, F. Dillen, L. Verstraelen, L. Vrancken, A pointwise inequality in submanifold theory. Arch. Math. (Brno) 35, 115–128 (1999)MathSciNetMATH P.J. De Smet, F. Dillen, L. Verstraelen, L. Vrancken, A pointwise inequality in submanifold theory. Arch. Math. (Brno) 35, 115–128 (1999)MathSciNetMATH
23.
Zurück zum Zitat S. Greenfield, Cauchy-Riemann equations in several variables. An. Scuola Norm. Sup. Pisa 22, 275–314 (1968)MathSciNetMATH S. Greenfield, Cauchy-Riemann equations in several variables. An. Scuola Norm. Sup. Pisa 22, 275–314 (1968)MathSciNetMATH
25.
Zurück zum Zitat S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. I, II (Interscience, New York, 1963, 1969) S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. I, II (Interscience, New York, 1963, 1969)
27.
Zurück zum Zitat K. Matsumoto, I. Mihai, Y. Tazawa, Ricci tensor of slant submanifolds in complex space forms. Kodai Math. J. 26, 85–94 (2003)MathSciNetCrossRefMATH K. Matsumoto, I. Mihai, Y. Tazawa, Ricci tensor of slant submanifolds in complex space forms. Kodai Math. J. 26, 85–94 (2003)MathSciNetCrossRefMATH
28.
Zurück zum Zitat A. Mihai, An inequality for totally real surfaces in complex space forms. Krag. J. Math. 26, 83–88 (2004)MathSciNetMATH A. Mihai, An inequality for totally real surfaces in complex space forms. Krag. J. Math. 26, 83–88 (2004)MathSciNetMATH
29.
30.
Zurück zum Zitat I. Mihai, Geometry of Submanifolds in Complex Manifolds (in Romanian) (Editura Universitatii din Bucureşti, 2001) I. Mihai, Geometry of Submanifolds in Complex Manifolds (in Romanian) (Editura Universitatii din Bucureşti, 2001)
32.
Zurück zum Zitat I. Mihai, On the generalized Wintgen inequality for Lagrangian submanifolds in complex space forms. Nonlinear Anal. 95, 714–720 (2014)MathSciNetCrossRefMATH I. Mihai, On the generalized Wintgen inequality for Lagrangian submanifolds in complex space forms. Nonlinear Anal. 95, 714–720 (2014)MathSciNetCrossRefMATH
33.
Zurück zum Zitat I. Mihai, A. Mihai, CR-submanifolds in complex space forms and Sasakian space forms, in Geometry of Cauchy-Riemann Submanifolds, ed. by S. Dragomir, M. Hasan Shahid, F. Al-Solamy (Springer, New York, 2016) I. Mihai, A. Mihai, CR-submanifolds in complex space forms and Sasakian space forms, in Geometry of Cauchy-Riemann Submanifolds, ed. by S. Dragomir, M. Hasan Shahid, F. Al-Solamy (Springer, New York, 2016)
34.
Zurück zum Zitat A. Oiagă, I. Mihai, B.Y. Chen inequalities for slant submanifolds in complex space forms. Demonstratio Math. 32, 835–846 (1999)MathSciNetMATH A. Oiagă, I. Mihai, B.Y. Chen inequalities for slant submanifolds in complex space forms. Demonstratio Math. 32, 835–846 (1999)MathSciNetMATH
35.
Zurück zum Zitat B. Rouxel, Sur une famille des A-surfaces d’un espace euclidien E \(^4\), Österreischer Mathematiker Kongress, Insbruck (1981), 185pp B. Rouxel, Sur une famille des A-surfaces d’un espace euclidien E \(^4\), Österreischer Mathematiker Kongress, Insbruck (1981), 185pp
36.
37.
Zurück zum Zitat B. Suceavă, On strongly minimal Kähler surfaces in C \(^3\) and the equality \(scal(p) = 4 \inf sec(\pi ^r)\). Results Math. 68, 45–69 (2015) B. Suceavă, On strongly minimal Kähler surfaces in C \(^3\) and the equality \(scal(p) = 4 \inf sec(\pi ^r)\). Results Math. 68, 45–69 (2015)
38.
Zurück zum Zitat W. Thurston, Some simple examples of symplectic manifolds. Proc. Am. Math. Soc. 55, 467–468 (1976)MathSciNetMATH W. Thurston, Some simple examples of symplectic manifolds. Proc. Am. Math. Soc. 55, 467–468 (1976)MathSciNetMATH
39.
Zurück zum Zitat P. Wintgen, Sur l’inégalité de Chen-Willmore. C. R. Acad. Sci. Paris Sér. A-B 288, A993–A995 (1979)MathSciNetMATH P. Wintgen, Sur l’inégalité de Chen-Willmore. C. R. Acad. Sci. Paris Sér. A-B 288, A993–A995 (1979)MathSciNetMATH
40.
Zurück zum Zitat K. Yano, S. Ishihara, The f-structures induced on submanifolds of complex and almost complex spaces. Kodai Math. Sem. Rep. 18, 271–292 (1966)MathSciNetCrossRefMATH K. Yano, S. Ishihara, The f-structures induced on submanifolds of complex and almost complex spaces. Kodai Math. Sem. Rep. 18, 271–292 (1966)MathSciNetCrossRefMATH
41.
Zurück zum Zitat K. Yano, M. Kon, Anti-Invariant Submanifolds (M. Dekker, New York, 1976)MATH K. Yano, M. Kon, Anti-Invariant Submanifolds (M. Dekker, New York, 1976)MATH
42.
Zurück zum Zitat K. Yano, M. Kon, CR-Submanifolds of Kaehlerian and Sasakian Manifolds (Birkhäuser, Basel, 1983)CrossRefMATH K. Yano, M. Kon, CR-Submanifolds of Kaehlerian and Sasakian Manifolds (Birkhäuser, Basel, 1983)CrossRefMATH
43.
Zurück zum Zitat K. Yano, M. Kon, Structures on Manifolds (World Scientific, Singapore, 1984)MATH K. Yano, M. Kon, Structures on Manifolds (World Scientific, Singapore, 1984)MATH
44.
Zurück zum Zitat F. Zheng, Complex Differential Geometry, AMS/IP Studies in Advanced Mathematics (2000) F. Zheng, Complex Differential Geometry, AMS/IP Studies in Advanced Mathematics (2000)
Metadaten
Titel
Special Submanifolds in Hermitian Manifolds
verfasst von
Ion Mihai
Copyright-Jahr
2017
DOI
https://doi.org/10.2991/978-94-6239-240-3_9