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On a compact n¡dimensional manifold Mn , a criti cal point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, sati .es the critical point equation (CPE), given by zg = s0¤g (f). It has been conjectured that a solution (g, f) of CPE is Einstein. The purpose of the present paper is to prove that every compact stable minimal hypersurface is in a certain hypersurface of Mn under an assumption that Ker(s0¤g ) = 0.
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참고문헌 (4)
참고문헌 신청
/ 1974 / Manifolds of Riemannian Metrics with Prescribed Scalar Curvature 80 : 479 ~ 484
/ 2000 / Critical points and conformally °at metrics 37 (3) : 641 ~ 648
/ 2000 / Critical points of the scalar curvature functionals on the space of metrics of constant scalar curvature 103 : 135 ~ 142
/ 2003 / The critical point equation on a three dimensional compact manifold 131 : 3221 ~ 3230
/ 2000 / Critical points and conformally °at metrics 37 (3) : 641 ~ 648
/ 2000 / Critical points of the scalar curvature functionals on the space of metrics of constant scalar curvature 103 : 135 ~ 142
/ 2003 / The critical point equation on a three dimensional compact manifold 131 : 3221 ~ 3230
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