On affine transformations of Banachable bundles
Efstathios Vassiliou (1981)
Colloquium Mathematicae
Vincze, Csaba (2008)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
Csaba Vincze, Tahere Reza Khoshdani, Sareh Mehdi Zadeh Gilani, Márk Oláh (2019)
Communications in Mathematics
In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.
Josef Mikeš, Sándor Bácsó, Josef Zedník (1997)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Lashin, El-Said R., Mersal, Tarek F. (2004)
International Journal of Mathematics and Mathematical Sciences
Lashin, El-Said R., Mersal, Tarek F. (2002)
International Journal of Mathematics and Mathematical Sciences
H. R. Salimi Moghaddam (2009)
Archivum Mathematicum
In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in...
Michor, P.W., Ratiu, T.S. (1998)
Journal of Lie Theory
Osmo Pekonen (1989)
Manuscripta mathematica
José Isidro (2007)
Open Mathematics
The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.
Erhard Neher (1992)
Mathematische Zeitschrift
S.T. Yau, R. Schoen (1979)
Manuscripta mathematica
Gustavo Corach (1994)
Banach Center Publications
Misha Gromov (2014)
Open Mathematics
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.
P. Assouad (1979/1980)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
Irving E. Segal (1986)
Revista Matemática Iberoamericana
The solution manifold M of the equation ⎯φ + gφ3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal...
Ballico, E. (2004)
Georgian Mathematical Journal
Galanis, George, Vassiliou, Efstathios (2004)
Balkan Journal of Geometry and its Applications (BJGA)
Peter W. Michor, David Mumford (2006)
Journal of the European Mathematical Society
We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from to the plane modulo the group of diffeomorphisms of , acting as reparametrizations. In particular we investigate the metric, for a constant , where is the curvature of the curve and , are normal vector fields to . The term is a sort of geometric Tikhonov regularization because, for , the geodesic distance between any two distinct curves is 0, while for the...
Hilsum, Michel (1999)
Annals of Mathematics. Second Series