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Ricci curvature of submanifolds of an S-space form

Mukut Mani Tripathi|김정식|Mohit Kumar Dwivedi
대한수학회 (The Korean Mathematical Society)|2009.09|대한수학회보 (Bulletin of the KMS)|제46권 제5호|pp. 979-998

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참고문헌

키워드

scalar curvatureRicci curvaturek-Ricci curvatureS-space formalmost semi-invariant submanifoldθ-slant submanifoldanti-invariant submanifoldθ-invaraint.
주제분류수학

초록

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, θ-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant θ_k of different kind of submanifolds of a S-space form M(c) are obtained.

Abstract

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, θ-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant θ_k of different kind of submanifolds of a S-space form M(c) are obtained.

참고문헌 (36)

  1. A. Bejancu, "Geometry of CR-Submanifolds" (1986), D. Reidel Publishing Co
  2. D. E. Blair, "Geometry of manifolds with structural group U(n) × O(s)", J. Differential Geometry, 4, pp.155~167 (1970)
  3. D. E. Blair, "On a generalization of the Hopf fibration", An. S¸ti. Univ. “Al. I. Cuza” Ia¸si Sect¸. I a Mat. (N.S.), 17, pp.171~177 (1971)
  4. D. E. Blair, "Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics", pp.203~ (2002), Birkhauser Boston, Inc
  5. D. E. Blair, "Differential geometric structures on principal toroidal bundles", Trans. Amer. Math. Soc, 181, pp.175~184 (1973)
  6. J. L. Cabrerizo, "A classification of totally fumbilical submanifolds of an S-manifold", Soochow J. Math, 18(2), pp.211~221 (1992)
  7. J. L. Cabrerizo, "The curvature of submanifolds of an S-space form", Acta Math. Hungar, 62(3), pp.373~383 (1993)
  8. J. L. Cabrerizo, "On certain anti-invariant submanifolds of an S-manifold", Portugal. Math, 50(1), pp.103~113 (1993)
  9. J. L. Cabrerizo, "On normal CR-submanifolds of S-manifolds", Colloq. Math, 64(2), pp.203~214 (1993)
  10. A. Carriazo, "Minimal slant submanifolds of the smallest dimension in S-manifolds", Rev. Mat. Iberoamericana, 21(1), pp.47~66 (2005)
  11. A. Carriazo, "Some slant submanifolds of S-manifolds", Acta Math. Hungar, 107(4), pp.267~285 (2005)
  12. B.-Y. Chen, "Mean curvature and shape operator of isometric immersions in real-spaceforms", Glasgow Math. J., 38, pp.87~97 (1996)
  13. B.-Y. Chen, "Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions", Glasg. Math. J, 41(1), pp.33~41 (1999)
  14. B.-Y. Chen, "On Ricci curvature of isotropic and Lagrangian submanifolds in complex space forms", Arch. Math. (Basel), 74(2), pp.154~160 (2000)
  15. B.-Y. Chen, "Riemannian submanifolds, Handbook of differential geometry", pp.187~418 (2000), North-Holland
  16. Luis M. Fern\'{a}ndez, "New Relationships involving the Mean Curvature of Slant Submanifolds in $S$-space-forms", 대한수학회지, 44(3), pp.647~659 (2007), 대한수학회
  17. S. P. Hong, "Certain basic inequalities for submanifolds of locally conformal Kaehler space forms", SUT J. Math, 41(1), pp.75~94 (2005)
  18. S. P. Hong, "On Ricci curvature of submanifolds of generalized Sasakian space forms", Int. J. Pure Appl. Math. Sci, 2(2), pp.173~201 (2005)
  19. S. P. Hong, "On Ricci curvature of submanifolds", Int. J. Pure Appl. Math. Sci, 2(2), pp.227~245 (2005)
  20. S. P. Hong, "Ricci curvature of submanifolds of a Sasakian space form", Iranian J. Math. Sci. Inform, 1(2), pp.31~51 (2006)
  21. T. Kashiwada, "On a Riemannian manifold admitting a framed f − 3-structure", Natur. Sci. Rep. Ochanomizu Univ, 22, pp.91~99 (1971)
  22. 김정식, "Ricci curvature of integral submanifolds of an $\mathcal{S}$-space form", 대한수학회보, 44(3), pp.395~406 (2007), 대한수학회
  23. M. Kobayashi, "Semi-invariant submanifolds in an f-manifold with complemented frames", Tensor (N.S.), 49(2), pp.154~177 (1990)
  24. M. Kobayashi, "Invariant submanifolds of an f-manifold with complemented frames", K¯odai Math. Sem. Rep, 24, pp.430~450 (1972)
  25. I. Mihai, "CR-submanifolds of a framed f-manifold", Stud. Cerc. Mat, 35(2), pp.127~136 (1983)
  26. I. Mihai, "Ricci curvature of submanifolds in Sasakian space forms", J. Aust. Math. Soc, 72(2), pp.247~256 (2002)
  27. H. Nakagawa, "On framed f-manifolds", K¯odai Math. Sem. Rep, 18, pp.293~306 (1966)
  28. B. Suceava, "Some remarks on B.-Y. Chen’s inequality involving classical invariants", An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.), 45(2), pp.405~412 (1999)
  29. M. M. Tripathi, "On almost semi-invariant submanifolds", 박사, pp.1996
  30. M. M. Tripathi, "Certain basic inequalities for submanifolds", Proceedings of the Tenth International Workshop on Differential Geometry, pp.99~145 (2006), Kyungpook Nat. Univ
  31. M. M. Tripathi, "Mean curvature and shape operator of slant immersions in a Sasakian space form", Balkan J. Geom. Appl, 7(1), pp.101~111 (2002)
  32. M. M. Tripathi, "Submanifolds of framed metric manifolds and S-manifolds", Note Mat, 20(2), pp.135~164 (2000)
  33. M. M. Tripathi, "semi-invariant submanifolds of an ²-framed metric manifold", Demonstratio Math, 29(2), pp.413~426 (1996)
  34. M. M. Tripathi, "On submanifolds of S-manifolds", Ganita, 47(2), pp.51~54 (1996)
  35. J. Vanzura, "Almost r-contact structures", Ann. Scuola Norm. Sup. Pisa, 26, pp.97~115 (1972)
  36. K. Yano, "Structures on Manifolds, Series in Pure Mathematics", pp.3~ (1984), World Scientific Publishing Co

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