Conformal fields and the stability of leaves with constant higher order mean curvature |
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| Authors: | Krzysztof Andrzejewski Pawe? G Walczak |
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| Institution: | aInstitute of Mathematics, Polish Academy of Sciences, ul. ?niadeckich 8, 00-956 Warszawa, Poland;bDepartment of Theoretical Physics II, University of ?ód?, ul. Pomorska 149/153, 90-236 ?ód?, Poland;cFaculty of Mathematics and Informatics, University of ?ód?, ul. Banacha 22, 90-238 ?ód?, Poland |
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| Abstract: | In this paper, we study hypersurfaces with constant rth mean curvature Sr. We investigate the stability of such hypersurfaces in the case when they are leaves of a codimension one foliation. We also generalize recent results by Barros and Sousa, concerning conformal fields, to an arbitrary manifold. Using this we show that normal component of a Killing field is an rth Jacobi field of a hypersurface with Sr+1 constant. Finally, we study relations between rth Jacobi fields and vector fields preserving a foliation. |
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| Keywords: | MSC: 53C12 53C42 |
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