Notes on Chen’s inequalities for submanifolds of real space forms with a semi-symmetric non-metric connection
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摘要: 利用代数技巧,得到了具有半对称非度量联络的实空间形式中的子流形的Chen广义不等式,推广了C. Ozgur和A. Mihai的一个结果.并订正了他们文章中的一个错误
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关键词:
- Chen广义不等式 /
- Chen-Ricci不等式 /
- 实空间形式 /
- 半对称非度量联络
Abstract: By using algebraic techniques, we proved Chens general inequalities for submanifolds of real space forms with a semi-symmetric non-metric connection, which generalized a result of C. Ozgur and A. Mihai. Also, a mistake of their paper has been modified.-
Key words:
- Chen′s general inequalities /
- Chen-Ricci inequalities /
- real space form /
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[1] CHEN B Y. Mean curvature and shape operator of isometric immersions in real space forms [J]. Glasgow Math J, 1996, 38(1): 87-97.NASH J F. The imbedding problem for Riemannian manifolds [J]. Ann Math, 1956, 63: 20-63.CHEN B Y, DILLEN F, VERSTRAELEN L, VRANCKEN L. Totally real submanifolds of CPn satisfying a basic equality [J]. Arch Math, 1994, 63: 553-564.CHEN B Y. δ-Invariants, Inequalities of submanifolds and their applications [J/OL]. arXiv preprint arXiv: 1307.1877, 2013.CHEN B Y. A tour through δ-invariants: From Nash's embedding theorem to ideal immersions, best ways of living and beyond [J/OL]. arXiv preprint arXiv: 1307.1030, 2013.CHERN S S. Minimal Submanifolds in a Riemannian Manifold [M]. University of Kansas Press, 1968.CHEN B Y. Some pinching and classification theorems for minimal submanifolds [J]. Arch Math, 1993, 60: 568-578.CHEN B Y. A Riemannian invariant and its application to submanifolds theory [J]. Results in Math, 1995, 27: 17-26.CHEN B Y. Ideal Lagrangian immersions in complex space forms [J]. Math Proc Cambridge Philos Soc, 2000, 128: 511-533.OPREA T. Chen's inequality in the Lagrangian case [J]. Colloq Math, 2007, 108: 163-169.CHEN B Y, DILLEN F. Optimal general inequalities for Lagrangian submanifolds in complex space forms [J]. J Math Anal Appl, 2011, 379: 229-239.CHEN B Y, DILLEN F. δ-invariants for Lagrangian submanifolds of complex space forms [C]. Riemannian Geometry and Applications-Proceedings RIGA. Univ Bucuresti, Bucharest, 2011: 75-94.CHEN B Y, DILLEN F, VAN DER VEKEN J, VRANCKEN L. Curvature inequalities for Lagrangian submanifolds: The final solution [J]. Differential Geometry and Its Applications, 2013, 31: 808-819.CHEN B Y. Pseudo-Riemannian Geometry, δ-Invariants and Application [M]. New Jersey: World Scientic, 2011.LI G, WU C. Slant immersions of complex space forms and Chen's inequality [J]. Acta Mathematica Scientia, 2005, 25B(2): 223-232.TRIPATHI M M, KIM J S, KIM S B. A note on Chen's basic equality for submanifolds in a Sasakian space form [J]. International Journal of Mathematics and Mathematical Sciences, 2003, 2003(11): 711-716.ARSLAN K, EZENTAS R, MIHAI I. ÖZGUR C. Certain inequalities for submanifolds in (k, μ)-contact space forms [J]. Bulletin of the Australian Mathematical Society, 2001, 64(2): 201-212.GULBHAR M, KILIC E, KELES S. Chen-like inequalities on lightlike hypersurfaces of a Lorentzian manifold [J]. Journal of Inequalities and Applications, 2013, 2013(1): 266.DILLEN F, PETROVIC M, VERSTRAELEN L. Einstein, conformally flat and semi-symmetric submanifolds satisfying Chen's equality [J]. Israel Journal of Mathematics, 1997, 100(1): 163-169.
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