• 대한수학회논문집
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• 제34권2호
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• pp.603-614
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• 2019

In the present paper, we derive two optimal inequalities for totally real submanifolds and C-totally real submanifolds of LCS-manifolds with respect to Levi-Civita connection and quarter symmetric metric connection by using T. Oprea's optimization method.

• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.167-182
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• 2018

In this paper, we prove the optimal inequalities for the generalized normalized ${\delta}$-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized (${\kappa},{\mu}$)-space forms. The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form. We also characterize the submanifolds on which equalities hold.

• 대한수학회보
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• 제52권5호
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• pp.1631-1647
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• 2015

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.