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Infinitesimal bending of a subspace of a space with non-symmetric basic tensor

Svetislav M. Minčić, Ljubica S. Velimirović (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this work infinitesimal bending of a subspace of a generalized Riemannian space (with non-symmetric basic tensor) are studied. Based on non-symmetry of the connection, it is possible to define four kinds of covariant derivative of a tensor. We have obtained derivation formulas of the infinitesimal bending field and integrability conditions of these formulas (equations).

On applications of the Yano–Ako operator

A. Magden, Arif A. Salimov (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we consider a method by which a skew-symmetric tensor field of type (1,2) in M n can be extended to the tensor bundle T q 0 ( M n ) ( q > 0 ) on the pure cross-section....

On Hermitian manifold with torsion.

Aruna Nigam (1979)

Revista Matemática Hispanoamericana

Analytic vector fields in a Hermitian manifold have been studied by various authors [3, 4, 6 & 7]. Boothby [2] and Goldberg [1] extended some of these results to Hermitian manifold with torsion. In this paper we define and study p-pseudo-analytic vector fields, which when p = 1, reduce to analytic vector fields as given in [1] and [2]. A necessary and sufficient condition for a vector field to be covariant (contravariant) p-pseudo-analytic has been obtained and their relationship with p-pseudo-harmonic...

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

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 systems appear...

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