First eigenvalue of Schrodinger operator of space-like hypersurfaces
نویسندگان
چکیده
منابع مشابه
Hypersurfaces of a Sasakian space form with recurrent shape operator
Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.
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ABSTRACT : The stability operator of a compact oriented minimal hypersurface Mn−1 ⊂ S is given by J = −∆ − ‖A‖ − (n − 1), where ‖A‖ is the norm of the second fundamental form. Let λ1 be the first eigenvalue of J and define β = −λ1 − 2(n − 1). In [S] Simons proved that β ≥ 0 for any non-equatorial minimal hypersurface M ⊂ S. In this paper we will show that β = 0 only for Clifford hypersurfaces. ...
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In this paper, we prove new pinching theorems for the first eigenvalue λ1(M) of the Laplacian on compact hypersurfaces of the Euclidean space. These pinching results are associated with the upper bound for λ1(M) in terms of higher order mean curvatures Hk. We show that under a suitable pinching condition, the hypersurface is diffeomorpic and almost isometric to a standard sphere. Moreover, as a...
متن کاملhypersurfaces of a sasakian space form with recurrent shape operator
let $(m^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the sasakian space form$widetilde{m}(c)$. we show that if the shape operator $a$ of $m$ isrecurrent then it is parallel. moreover, we show that $m$is locally a product of two constant $phi-$sectional curvaturespaces.
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ژورنال
عنوان ژورنال: ANZIAM Journal
سال: 2010
ISSN: 1445-8810
DOI: 10.21914/anziamj.v51i0.1618