OPTIMAL INEQUALITIES FOR THE CASORATI CURVATURES OF SUBMANIFOLDS OF GENERALIZED SPACE FORMS ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTIONS

키워드

참고문헌 (43)

1. L. Albertazzi, "Handbook of Experimental Phenomenology: Visual Perception of Shape, Space and Apearance" (2013), Wiley
2. P. Alegre, "Generalized Sasakian space form", Israel J. Math, 141(1), pp.157~183 (2004)
3. P. Alegre, "B. Y. Chen’s inequality for submanifolds of generalized space forms", Indian J. Pure Appl. Math, 38(3), pp.185~201 (2007)
4. D. E. Blair, "The theory of quasi-Sasakian structures", J. Differential Geom, 1, pp.331~345 (1967)
5. D. E. Blair, "Quasi-umbilical, minimal submanifolds of Euclidean space", Simon Stevin, 51(1), pp.3~22 (1977)
6. F. Casorati, "Mesure de la courbure des surfaces suivant l’id´ee commune. Ses rapports avec les mesures de courbure gaussienne et moyenne", Acta Math, 14(1), pp.95~110 (1890)
7. B.-Y. Chen, "Some pinching and classification theorems for minimal submanifolds", Arc. Math. (Basel), 60(6), pp.568~578 (1993)
8. B.-Y. Chen, "Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions", Glasg. Math. J, 41(1), pp.33~41 (1999)
9. B.-Y. Chen, "An optimal inequality for CR-warped products in complex space forms involving CR δ-invariant", Internat. J. Math, 23(3), pp.1250045~ (2012)
10. B.-Y. Chen, "Optimal general inequalities for Lagrangian submanifolds in complex space forms", J. Math. Anal. Appl, 379(1), pp.229~239 (2011)
11. B.-Y. Chen, "Curvature inequalities for Lagrangian submanifolds: the final solution", Differential Geom. Appl, 31(6), pp.808~819 (2013)
12. S. Decu, "Optimal inequalities involving Casorati curvatures", Bull. Transylv. Univ. Brasov, Ser. B, 14(49)(Suppl), pp.85~93 (2007)
13. S. Decu, "Optimal inequalities charaterising quasi-umbilical submanifolds", J. Inequal. Pure Appl. Math, 9(3), pp.7~ (2008)
14. A. Friedmann, "¨Uber die Geometrie der halbsymmetrischen", ¨Ubertragungen, Math. Z, 21(1), pp.211~223 (1924)
15. S. Haesen, "On the extrinsic principal directions of Riemannian submanifolds", Note Math, 29(2), pp.41~53 (2009)
16. H. A. Hayden, "Subspaces of a space with torsion", Proc. London Math. Soc, 34, pp.27~50 (1932)
17. S. Hong, "On Ricci curvature of submanifolds of generalized Sasakian space forms", Int. J. Pure Appl. Math. Sci, 2(2), pp.173~201 (2005)
18. T. Imai, "Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection", Tensor (N. S.), 23, pp.300~306 (1972)
19. T. Imai, "Notes on semi-symmetric metric connections", Tensor (N. S.), 24, pp.293~296 (1972)
20. D. Janssens, "Almost contact structures and curvature tensors", Kodai Math. J, 4(1), pp.1~27 (1981)
21. K. Kenmotsu, "A class of almost contact Riemannian manifolds", Tˇohoku Math. J, 24, pp.93~103 (1972)
22. 김정식, "Chen inequalities for submanifolds in generalized complex space forms", 대한수학회보, 40(3), pp.411~423 (2003), 대한수학회
23. J.W. Lee, "Inequalities for generalized normalized δ-Casorati Curvatures of slant submanifolds in quaternionic space forms", Taiwanese J. Math, 19(3), pp.691~702 (2015)
24. R. Lemence, "On four-dimensional generalized complex space forms", Nihonkai Math. J, 15(2), pp.169~176 (2004)
25. G. D. Ludden, "Submanifolds of cosymplectic manifolds", J. Differential Geometry, 4, pp.237~244 (1970)
26. J. C. Marrero, "The local structure of trans-Sasakian manifolds", Ann. Mat. Pure Appl, 162, pp.77~86 (1992)
27. K. Matsumoto, "Ricci tensor of slant submanifolds in complex space forms", Kodai Math. J, 26(1), pp.85~94 (2003)
28. A. Mihai, "Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection", Taiwanese J. Math, 14(4), pp.1465~1477 (2010)
29. A. Mihai, "Chen inequalities for submanifolds of complex space forms and Sasakian space forms endowed with semi-symmetric metric connections", Rocky Mountain J. Math, 41(5), pp.1653~1673 (2011)
30. Z. Nakao, "Submanifolds of a Riemannian manifold with semi-symmetric metric connections", Proc. Amer. Math. Soc, 54, pp.261~266 (1976)
31. A. Oiaga, "B.-Y. Chen inequalities for slant submanifolds in complex space forms", Demonstratio Math, 32(4), pp.835~846 (1999)
32. Z. Olszak, "On the existence of generalized complex space forms", Israel J. Math, 65(2), pp.214~218 (1989)
33. J. A. Oubina, "New classes of almost contact metric structures", Publ. Math. Debrecen, 32(3-4), pp.187~193 (1985)
34. V. Slesar, "Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms", J. Inequal. Appl, 2014, pp.123~ (2014)
35. F. Tricerri, "Curvature tensors on almost Hermitian manifolds", Trans. Amer. Math. Soc, 267(2), pp.365~398 (1981)
36. M. M. Tripathi, "Generic submanifolds of generalized complex space forms", Publ. Math. Debrecen, 50(3-4), pp.373~392 (1997)
37. M. M. Tripathi, "A new connection in a Riemannian manifold", Int. Electron. J. Geom, 1(1), pp.15~24 (2008)
38. M. M. Tripathi, "Ricci curvature and k-Ricci curvature of submanifolds of generalized complex space forms", Aligarh Bull. Math, 20(1), pp.143~156 (2001)
39. L. Verstraelen, "The geometry of eye and brain", Soochow J. Math, 30(3), pp.367~376 (2004)
40. L. Verstraelen, "Geometry of submanifolds I, The first Casorati curvature indicatrices", Kragujevac J. Math, 37(1), pp.5~23 (2013)
41. K. Yano, "On semi-symmetric metric connection", Rev. Roumaine Math. Pure Appl, 15, pp.1579~1586 (1970)
42. D. W. Yoon, "Inequality for warped products in generalized Sasakian space forms", Int. Math. J, 5(3), pp.225~235 (2004)
43. P. Zhang, "Chen's inequalities for submanifolds of a Riemannian manifold of quasi-constatnt curvature with a semi-symmetric metric connection", Taiwanese J. Math, 18(6), pp.1841~1862 (2014)

관련 논문AI추천