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In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.
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참고문헌 (28)
참고문헌 신청
A. Friedmann / 1924 / ¨Uber die Geometrie der halbsymmetrischen / ¨Ubertragungen, Math. Z 21 (1) : 211 ~ 223
A. Mihai / 2010 / Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection / Taiwanese J. Math 14 (4) : 1465 ~ 1477
B.-Y. Chen / 1993 / Some pinching and classification theorems for minimal submanifolds / Arc. Math. (Basel) 60 (6) : 568 ~ 578
B.-Y. Chen / 1999 / Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions / Glasg. Math. J 41 (1) : 33 ~ 41
B.-Y. Chen / 2011 / Optimal general inequalities for Lagrangian submanifolds in complex space forms / J. Math. Anal. Appl 379 (1) : 229 ~ 239
A. Mihai / 2010 / Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection / Taiwanese J. Math 14 (4) : 1465 ~ 1477
B.-Y. Chen / 1993 / Some pinching and classification theorems for minimal submanifolds / Arc. Math. (Basel) 60 (6) : 568 ~ 578
B.-Y. Chen / 1999 / Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions / Glasg. Math. J 41 (1) : 33 ~ 41
B.-Y. Chen / 2011 / Optimal general inequalities for Lagrangian submanifolds in complex space forms / J. Math. Anal. Appl 379 (1) : 229 ~ 239
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