A Classification of Parallel Normalized Biconservative Submanifold in the Minkowski Space in Arbitrary Dimension

Authors : Aykut Kayhan

Pages : 653-664

Doi:10.36890/iejg.1263203

View : 139 | Download : 164

Publication Date : 2023-10-29

Article Type : Research Paper

Abstract :IIn this paper, we examine PNMCV-MCGL biconservative submanifold in a Minkowski space $\\mathbb{E}_1^{n+2}$ with nondiagonalizable shape operator, where PNMCV-MCGL submanifold denotes a submanifold with parallel normalized mean curvature vector and the mean curvature whose gradient is lightlike ($\\langle\\nabla H,\\nabla H\\rangle=0$). We obtain some conditions about connection forms, principal curvatures and some results about them. Then we use them to obtain a classification of such submanifolds. Finally, we showed that there is no biconservative such submanifold in Minkowski space of arbitrary dimension.
Keywords : Biconservative submanifolds, non diagonalizable shape operator, Minkowski space, biconservative isometric immersions

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