A basic inequality for submanifolds in locally conformal almost cosymplectic manifolds |
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Authors: | Mukut Mani Tripathi Jeong-Sik Kim Seon-Bu Kim |
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Institution: | (1) Department of Mathematics and Astronomy, Lucknow University, 226 007 Lucknow, India;(2) Department of Mathematics Education, Sunchon National University, 540-742 Sunchon, Korea;(3) Department of Mathematics, Chonnam National University, 500-757 Kwangju, Korea |
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Abstract: | For submanifolds tangent to the structure vector field in locally conformal almost cosymplectic manifolds of pointwise constantφ-sectional curvature, we establish a basic inequality between the main intrinsic invariants of the submanifold on one side,
namely its sectional curvature and its scalar curvature; and its main extrinsic invariant on the other side, namely its squared
mean curvature. Some applications including inequalities between the intrinsic invariantδ
M
and the squared mean curvature are given. The equality cases are also discussed. |
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Keywords: | Locally conformal almost cosymplectic manifold invariant submanifold semi-invariant submanifold δ M -invariant squared mean curvature |
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