Abstract
Certain basic inequalities, involving the squared mean curvature and one of the scalar curvature, the sectional curvature and the Ricci curvature for a submanifold of any Riemannian manifold, are obtained. Applying these results we obtain the corresponding inequalities for different kinds of submanifolds of a locally conformal Kaehler space form. Equality cases are also discussed. Finally, we also find a sufficient condition for a Lagrangian submanifold of a locally conformal Kaehler space form to be minimal.
Funding Statement
First author was partially supported by Com2Mac-KOSEF. This work was finally completed while the third author visited as a guest researcher at Department of Mathematics Education, Faculty of Education, Yamagata University.
Acknowledgements
The authors are thankful to the referee for some comments towards the improvement of the paper.
Citation
Sungpyo Hong. Koji Matsumoto. Mukut Mani Tripathi. "Certain basic inequalities for submanifolds of locally conformal Kaehler space forms." SUT J. Math. 41 (1) 75 - 94, January 2005. https://doi.org/10.55937/sut/1126267696
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