Maxwell's equations in the Debye potential formalism
Mean and scalar curvature homogeneous Riemannian manifolds.
Metric of special 2F-flat Riemannian spaces
In this paper we find the metric in an explicit shape of special -flat Riemannian spaces , i.e. spaces, which are -planar mapped on flat spaces. In this case it is supposed, that is the cubic structure: .
Métriques riemanniennes holomorphes en petite dimension
Nous étudions les métriques riemanniennes holomorphes sur les variétés complexes compactes de dimension . Nous montrons que, contrairement au cas réel, une métrique riemannienne holomorphe possède un “grand” pseudo-groupe d’isométries locales. Ceci implique qu’une telle métrique n’existe pas sur les variétés complexes compactes simplement connexes de dimension .
Metrische Zusammenhänge und Torsion bei einfachen p-Vektoren.
Metrizability of connections on two-manifolds
We contribute to the reverse of the Fundamental Theorem of Riemannian geometry: if a symmetric linear connection on a manifold is given, find non-degenerate metrics compatible with the connection (locally or globally) if there are any. The problem is not easy in general. For nowhere flat -manifolds, we formulate necessary and sufficient metrizability conditions. In the favourable case, we describe all compatible metrics in terms of the Ricci tensor. We propose an application in the calculus of...
Metrization of connections with regular curvature
We discuss Riemannian metrics compatible with a linear connection that has regular curvature. Combining (mostly algebraic) methods and results of [4] and [5] we give an algorithm which allows to decide effectively existence of positive definite metrics compatible with a real analytic connection with regular curvature tensor on an analytic connected and simply connected manifold, and to construct the family of compatible metrics (determined up to a scalar multiple) in the affirmative case. We also...
Metrization problem for linear connections and holonomy algebras
We contribute to the following: given a manifold endowed with a linear connection, decide whether the connection arises from some metric tensor. Compatibility condition for a metric is given by a system of ordinary differential equations. Our aim is to emphasize the role of holonomy algebra in comparison with certain more classical approaches, and propose a possible application in the Calculus of Variations (for a particular type of second order system of ODE’s, which define geodesics of a linear...
Minimal lightlike hypersurfaces in with integrable screen distribution.
Minimal submanifolds in with a g.c.K. structure
In this paper we obtain all invariant, anti-invariant and submanifolds in endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.
Minimal Submanifolds in SN and RN.
Minimal surfaces in a complex projective space whose mean curvature vectors are eigenvectors.
Minkowski asymptotic spaces in general relativity
Minkowski minimal surfaces in with minimal focal surfaces.
Mixed covariant derivative and conjugate connections
Natural and projectively invariant quantizations on supermanifolds.
Natural intrinsic geometrical symmetries.
Natural transformations of 2-quasijets
Natural Transformations of Symmetric Affine Connections on Manifolds to Metrics on Linear Frame Bundles: a Classification.
Neifeld’s Connection Inducedon the Grassmann Manifold
The work concerns to investigations in the field of differential geometry. It is realized by a method of continuations and scopes of G. F. Laptev which generalizes a moving frame method and Cartan’s exterior forms method and depends on calculation of exterior differential forms. The Grassmann manifold (space of all -planes) is considered in the -dimensional projective space . Principal fiber bundle of tangent linear frames is arised above this manifold. Typical fiber of the principal fiber bundle...