Principal curvatures

Xem 1-4 trên 4 kết quả Principal curvatures
  • In this paper we give a new proof for the classification result in [3]. We show that isoparametric hypersurfaces with four distinct principal curvatures in spheres are of Clifford type provided that the multiplicities m1 , m2 of the principal curvatures satisfy m2 ≥ 2m1 − 1. This inequality is satisfied for all but five possible pairs (m1 , m2 ) with m1 ≤ m2 .

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  • Let M be an isoparametric hypersurface in the sphere S n with four distinct principal curvatures. M¨nzner showed that the four principal curvatures can u have at most two distinct multiplicities m1 , m2 , and Stolz showed that the pair (m1 , m2 ) must either be (2, 2), (4, 5), or be equal to the multiplicities of an isoparametric hypersurface of FKM-type, constructed by Ferus, Karcher and M¨nzner from orthogonal representations of Clifford algebras. In this paper, u we prove that if the multiplicities satisfy m2 ≥ 2m1 − 1, then the isoparametric hypersurface M must be...

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  • Invariant measures for the geodesic flow on the unit tangent bundle of a negatively curved Riemannian manifold are a basic and well-studied subject. This paper continues an investigation into a 2-dimensional analog of this flow for a 3-manifold N . Namely, the article discusses 2-dimensional surfaces immersed into N whose product of principal curvature equals a constant k between 0 and 1, surfaces which are called k-surfaces.

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  • This book is based on lectures delivered over the years by the author at the Universit´e Pierre et Marie Curie, Paris, at the University of Stuttgart, and at City University of Hong Kong. Its two-fold aim is to give thorough introductions to the basic theorems of differential geometry and to elasticity theory in curvilinear coordinates. The treatment is essentially self-contained and proofs are complete.

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