Page 1 Next

Displaying 1 – 20 of 1286

Showing per page

( h , Φ ) -entropy differential metric

María Luisa Menéndez, Domingo Morales, Leandro Pardo, Miquel Salicrú (1997)

Applications of Mathematics

Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on ( h , Φ ) -entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic...

4-dimensional anti-Kähler manifolds and Weyl curvature

Jaeman Kim (2006)

Czechoslovak Mathematical Journal

On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.

A characterization of isometries between Riemannian manifolds by using development along geodesic triangles

Petri Kokkonen (2012)

Archivum Mathematicum

In this paper we characterize the existence of Riemannian covering maps from a complete simply connected Riemannian manifold ( M , g ) onto a complete Riemannian manifold ( M ^ , g ^ ) in terms of developing geodesic triangles of M onto M ^ . More precisely, we show that if A 0 : T | x 0 M T | x ^ 0 M ^ is some isometric map between the tangent spaces and if for any two geodesic triangles γ , ω of M based at x 0 the development through A 0 of the composite path γ · ω onto M ^ results in a closed path based at x ^ 0 , then there exists a Riemannian covering map...

A characterization of n-dimensional hypersurfaces in R n + 1 with commuting curvature operators

Yulian T. Tsankov (2005)

Banach Center Publications

Let Mⁿ be a hypersurface in R n + 1 . We prove that two classical Jacobi curvature operators J x and J y commute on Mⁿ, n > 2, for all orthonormal pairs (x,y) and for all points p ∈ M if and only if Mⁿ is a space of constant sectional curvature. Also we consider all hypersurfaces with n ≥ 4 satisfying the commutation relation ( K x , y K z , u ) ( u ) = ( K z , u K x , y ) ( u ) , where K x , y ( u ) = R ( x , y , u ) , for all orthonormal tangent vectors x,y,z,w and for all points p ∈ M.

A characterization of the Riemann extension in terms of harmonicity

Cornelia-Livia Bejan, Şemsi Eken (2017)

Czechoslovak Mathematical Journal

If ( M , ) is a manifold with a symmetric linear connection, then T * M can be endowed with the natural Riemann extension g ¯ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to g ¯ initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure 𝒫 on ( T * M , g ¯ ) and prove that 𝒫 is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if g ¯ reduces to the...

A class of metrics on tangent bundles of pseudo-Riemannian manifolds

H. M. Dida, A. Ikemakhen (2011)

Archivum Mathematicum

We provide the tangent bundle T M of pseudo-Riemannian manifold ( M , g ) with the Sasaki metric g s and the neutral metric g n . First we show that the holonomy group H s of ( T M , g s ) contains the one of ( M , g ) . What allows us to show that if ( T M , g s ) is indecomposable reducible, then the basis manifold ( M , g ) is also indecomposable-reducible. We determine completely the holonomy group of ( T M , g n ) according to the one of ( M , g ) . Secondly we found conditions on the base manifold under which ( T M , g s ) ( respectively ( T M , g n ) ) is Kählerian, locally symmetric or Einstein...

Currently displaying 1 – 20 of 1286

Page 1 Next