Displaying similar documents to “Extension of Bochner-Lichnérowicz formula on spheres”

On tensor functions whose gradients have some skew-symmetries

Adriano Montanaro (1991)

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

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Let V n be a real inner product space of any dimension; and let Q α 1 ⁢ … ⁢ α v = Q ⌃ α 1 ⁢ … ⁢ α v ⁢ X β ⁢ 1 ⁢ … ⁢ β τ be a C 2 -map relating any two tensor spaces on V n . We study the consequences imposed on the form of this function by the condition that its gradient should be skew-symmetric with respect to some pairs α μ , β η of indexes. Any such a condition is written as a system of linear partial differential equations, with constant coefficients, which is symmetric with respect to certain couples of independent variables. The solutions of these...

Metrizability of connections on two-manifolds

Alena Vanžurová, Petra Žáčková (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We contribute to the reverse of the Fundamental Theorem of Riemannian geometry: if a symmetric linear connection on a manifold is given, find non-degenerate metrics compatible with the connection (locally or globally) if there are any. The problem is not easy in general. For nowhere flat 2 -manifolds, we formulate necessary and sufficient metrizability conditions. In the favourable case, we describe all compatible metrics in terms of the Ricci tensor. We propose an application in the...

Tensor product in symmetric function spaces.

S. V. Astashkin (1997)

Collectanea Mathematica

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A concept of the multiplicator of symmetric function space concerning to projective tensor product is introduced and studied. This allows us to obtain some concrete results. In particular, the well-know theorem of R. O'Neil about boundedness of tensor product in the Lorentz spaces Lpq is discussed.