Displaying similar documents to “Normal form of the NK-curvature operators”

Some existence results for the scalar curvature problem via Morse theory

Andrea Malchiodi (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove existence of positive solutions for the equation - g 0 u + u = 1 + ϵ K x u 2 * - 1 on S n , arising in the prescribed scalar curvature problem. is the Laplace-Beltrami operator on S n , 2 is the critical Sobolev exponent, and ϵ is a small parameter. The problem can be reduced to a finite dimensional study which is performed with Morse theory.

Topological tools for the prescribed scalar curvature problem on S n

Dina Abuzaid, Randa Ben Mahmoud, Hichem Chtioui, Afef Rigane (2014)

Open Mathematics

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In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

An example for the holomorphic sectional curvature of the Bergman metric

Żywomir Dinew (2010)

Annales Polonici Mathematici

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We study the behaviour of the holomorphic sectional curvature (or Gaussian curvature) of the Bergman metric of planar annuli. The results are then utilized to construct a domain for which the curvature is divergent at one of its boundary points and moreover the upper limit of the curvature at that point is maximal possible, equal to 2, whereas the lower limit is -∞.

Isotropic curvature: A survey

Harish Seshadri (2007-2008)

Séminaire de théorie spectrale et géométrie

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We discuss the notion of isotropic curvature of a Riemannian manifold and relations between the sign of this curvature and the geometry and topology of the manifold.