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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

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.

Some framed f -structures on transversally Finsler foliations

Cristian Ida (2011)

Annales UMCS, Mathematica

Some problems concerning to Liouville distribution and framed f-structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f(3, ε)-structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

Some functorial prolongations of general connections

Ivan Kolář (2018)

Archivum Mathematicum

We consider the problem of prolongating general connections on arbitrary fibered manifolds with respect to a product preserving bundle functor. Our main tools are the theory of Weil algebras and the Frölicher-Nijenhuis bracket.

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