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2013•Journal of MathematicsOpen access

THE COMPACT SUBMANIFOLD IN A LOCALLY-SYMMETRIC SPACE

HU You-jin

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Abstract

In this paper, the compact submanifold in a locally-symmetric space is researched. By calculating the Laplacian about the square of the norm of the second fundamental form of submanifolds, a necessary condition on the compact submanifold in a locally-symmetric space is given without the condition with parallel mean curvature vectorand minimal, which can generalize and improve the outer space of totally geodesic in a locally-symmetric space.

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What this paper is about

In this paper, the compact submanifold in a locally-symmetric space is researched. By calculating the Laplacian about the square of the norm of the second fundamental form of submanifolds, a necessary condition on the compact submanifold in a locally-symmetric space is given without the condition with parallel mean curvature vectorand minimal, which can generalize and improve the outer space of totally geodesic in a locally-symmetric space.

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Available abstract

In this paper, the compact submanifold in a locally-symmetric space is researched. By calculating the Laplacian about the square of the norm of the second fundamental form of submanifolds, a necessary condition on the compact submanifold in a locally-symmetric space is given without the condition with parallel mean curvature vectorand minimal, which can generalize and improve the outer space of totally geodesic in a locally-symmetric space.

Key concepts: Submanifold, Mathematics, Symmetric space, Totally geodesic, Second fundamental form, Pure mathematics, Mathematical analysis, Space (punctuation)

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