COMPACT HYPERSURFACES IN EUCLIDEAN SPACE AND SOME INEQUALITIES

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BEKTAS D.; ERGUT M.

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ISSN: 2588-4824

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Journal: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE Year:2006 | Volume:30 | Issue:A3 Page(s): 285-289

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Title

COMPACT HYPERSURFACES IN EUCLIDEAN SPACE AND SOME INEQUALITIES

Author(s)

BEKTAS D. | ERGUT M. | Issue Writer Certificate

Keywords

FIRST EIGENVALUE

SUPPORT FUNCTION

Abstract

Let (M,g) be a compact immersed hypersurface of (Rn+1,<,>), l1 the first nonzero eigenvalue, a the mean curvature, P the SUPPORT FUNCTION, A the shape operator, vol(M) the volume of M, and S the scalar curvature of M. In this paper, we established some eigenvalue inequalities and proved the above.1/n òM \\A\\2 P2DV ³ </span></p>M a2 P2 dV. 2 òM a2 P2 dV ³ 1/n (n-1) òM sp2 dV.If the scalar curvature S and the first nonzero eigenvalue l1 staisfy S= l1 (N-1), than òM [a2 - l1/n] p2 dv³ 0, 4) Suppose that the Ricci curvature of M is bounded below by a positive constant k. ThusòM a2 P2 dV ³ k/n(n-1) òM \\ gradf\\ dv+vol(M). 5) Suppose that the Ricci curvature is bounded and the scalar curvature satisfy S= l1(n− 1) and L=k- 2S>0 is a constant. Thusvol (M) ³ kl1 /L òM\\ Y \\ a pdv – 2S/L òM a2 P2 Dv.

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APA: Copy

BEKTAS, D., & ERGUT, M.. (2006). COMPACT HYPERSURFACES IN EUCLIDEAN SPACE AND SOME INEQUALITIES. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, 30(A3), 285-289. SID. https://sid.ir/paper/545414/en

Vancouver: Copy

BEKTAS D., ERGUT M.. COMPACT HYPERSURFACES IN EUCLIDEAN SPACE AND SOME INEQUALITIES. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE[Internet]. 2006;30(A3):285-289. Available from: https://sid.ir/paper/545414/en

IEEE: Copy

D. BEKTAS, and M. ERGUT, “COMPACT HYPERSURFACES IN EUCLIDEAN SPACE AND SOME INEQUALITIES,” IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, vol. 30, no. A3, pp. 285–289, 2006, [Online]. Available: https://sid.ir/paper/545414/en

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