A smooth gauge model on tangent bundle.
A special nonlinear connection in second order geometry.
A study on the one parameter Lorentzian spherical motions.
A symplectic reduction for pseudo-Riemannian manifolds with compatible almost product structures.
A Tour Through -invariants: from Nash’s Embedding Theorem to Ideal Immersions, Best Ways of Living and Beyond
A- субпланарные многообразия как вещественные реализации пространств над алгебрами
Abel's Theorem and Webs.
About twistor spinors with zero in Lorentzian geometry.
Affin manifolds with nilpotent holonomy.
Affine analogues of the Sasaki-Shchepetilov connection
For two-dimensional manifold M with locally symmetric connection ∇ and with ∇-parallel volume element vol one can construct a flat connection on the vector bundle TM ⊕ E, where E is a trivial bundle. The metrizable case, when M is a Riemannian manifold of constant curvature, together with its higher dimension generalizations, was studied by A.V. Shchepetilov [J. Phys. A: 36 (2003), 3893-3898]. This paper deals with the case of non-metrizable locally symmetric connection. Two flat connections on...
Affine reductive spaces
Affine surfaces with parallel shape operators
We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.
Affine surfaces with planar affine normals in 3-dimensional Minkowski space .
Algebraic geometry and local differential geometry
Algebraic restrictions on geometric realizations of curvature models
We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders,...
Algebraic theory of affine curvature tensors
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally appear in relative hypersurface theory.
Almost complex projective structures and their morphisms
We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical generalizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of the so called Weyl connections and preserving of this class turns out to be the necessary and sufficient...
Almost Complex Structure in the Frame Bundle of an Almost Contact Metric Manifold.
Almost contact manifolds with specified affine connexions III
Almost cosymplectic real hypersurfaces in Kähler manifolds