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Obata’s Rigidity Theorem for Metric Measure Spaces

Christian Ketterer (2015)

Analysis and Geometry in Metric Spaces

We prove Obata’s rigidity theorem for metric measure spaces that satisfy a Riemannian curvaturedimension condition. Additionally,we show that a lower bound K for the generalizedHessian of a sufficiently regular function u holds if and only if u is K-convex. A corollary is also a rigidity result for higher order eigenvalues.

On ( 1 , 1 ) -tensor fields on symplectic manifolds

Anton Dekrét (1999)

Archivum Mathematicum

Two symplectic structures on a manifold M determine a (1,1)-tensor field on M . In this paper we study some properties of this field. Conversely, if A is (1,1)-tensor field on a symplectic manifold ( M , ω ) then using the natural lift theory we find conditions under which ω A , ω A ( X , Y ) = ω ( A X , Y ) , is symplectic.

On 1-harmonic functions.

Wei, Shihshu Walter (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On 2 p -dimensional Riemannian manifolds with positive scalar curvature

Domenico Perrone (1984)

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

In questo lavoro si danno alcuni risultati sugli spettri degli operatori di Laplace per varietà Riemanniane compatte con curvatura scalare positiva e di dimensione 2 p . Ad essi si aggiunge una osservazione riguardante la congettura di Yamabe.

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