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Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

Wladimir G. Boskoff, Bogdan D. Suceavă (2008)

Czechoslovak Mathematical Journal

In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian's metrization procedure can be relaxed. Then, we prove that Barbilian's metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.

Basic equations of G -almost geodesic mappings of the second type, which have the property of reciprocity

Mića S. Stanković, Milan L. Zlatanović, Nenad O. Vesić (2015)

Czechoslovak Mathematical Journal

We study G -almost geodesic mappings of the second type θ π 2 ( e ) , θ = 1 , 2 between non-symmetric affine connection spaces. These mappings are a generalization of the second type almost geodesic mappings defined by N. S. Sinyukov (1979). We investigate a special type of these mappings in this paper. We also consider e -structures that generate mappings of type θ π 2 ( e ) , θ = 1 , 2 . For a mapping θ π 2 ( e , F ) , θ = 1 , 2 , we determine the basic equations which generate them.

Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product

Antonio W. Cunha, Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Lima Jr., Adriano A. Medeiros (2016)

Studia Mathematica

Our purpose is to apply suitable maximum principles in order to obtain Bernstein type properties for two-sided hypersurfaces immersed with constant mean curvature in a Killing warped product M × ρ , whose curvature of the base Mⁿ satisfies certain constraints and whose warping function ρ is concave on Mⁿ. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, L¹-Liouville. Rigidity results related to entire...

Biharmonic Riemannian maps

Bayram Ṣahin (2011)

Annales Polonici Mathematici

We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo-umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions on the target manifolds.

Bi-Legendrian connections

Beniamino Cappelletti Montano (2005)

Annales Polonici Mathematici

We define the concept of a bi-Legendrian connection associated to a bi-Legendrian structure on an almost -manifold M 2 n + r . Among other things, we compute the torsion of this connection and prove that the curvature vanishes along the leaves of the bi-Legendrian structure. Moreover, we prove that if the bi-Legendrian connection is flat, then the bi-Legendrian structure is locally equivalent to the standard structure on 2 n + r .

Bochner's formula for harmonic maps from Finsler manifolds

Jintang Li (2008)

Colloquium Mathematicae

Let ϕ :(M,F)→ (N,h) be a harmonic map from a Finsler manifold to any Riemannian manifold. We establish Bochner's formula for the energy density of ϕ and maximum principle on Finsler manifolds, from which we deduce some properties of harmonic maps ϕ.

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