| Autor: |
Li, Yanlin, Turki, Nasser Bin, Deshmukh, Sharief, Belova, Olga |
| Předmět: |
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| Zdroj: |
AIMS Mathematics; 2024, Vol. 9 Issue 10, p1-14, 14p |
| Abstrakt: |
Given an immersed hypersurface M n in the Euclidean space E n + 1 , the tangential component ω of the position vector field of the hypersurface is called the basic vector field, and the smooth function of the normal component of the position vector field gives a function σ on the hypersurface called the support function of the hypersurface. In the first result, we show that on a complete and simply connected hypersurface M n in E n + 1 of positive Ricci curvature with shape operator T invariant under ω and the support function σ satisfies the static perfect fluid equation if and only if the hypersurface is isometric to a sphere. In the second result, we show that a compact hypersurface M n in E n + 1 with the gradient of support function σ , an eigenvector of the shape operator T with eigenvalue function the mean curvature H , and the integral of the squared length of the gradient ∇ σ has a certain lower bound, giving a characterization of a sphere. In the third result, we show that a compact and simply connected hypersurface M n of positive Ricci curvature in E n + 1 has an incompressible basic vector field ω , if and only if M n is isometric to a sphere. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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