The volumes of small geodesic balls for a metric connection
The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles
Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers, Élie Cartan...
Theorems concerning certain special tensor fields on Riemannian manifolds and their applications.
Theory of semisymmetric conformally flat and biharmonic submanifolds.
Theory of the zero order effect suitable to investigate the space-time geometrical properties.
TheStructure of Nearly Kähler Manifolds.
Three dimensional near-horizon metrics that are Einstein-Weyl
We investigate which three dimensional near-horizon metrics admit a compatible 1-form such that defines an Einstein-Weyl structure. We find explicit examples and see that some of the solutions give rise to Einstein-Weyl structures of dispersionless KP type and dispersionless Hirota (aka hyperCR) type.
Timelike -slant helices in Minkowski space
We consider a unit speed timelike curve in Minkowski 4-space and denote the Frenet frame of by . We say that is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction of . In this work we study those helices where the function is constant and we give different characterizations of such curves.
Timelike quaternion frame of a non-lightlike curve.
Torsion and the second fundamental form for distributions
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry.
Torsion Free Connections, Topology, Geometry and Differential Operators on Smooth Manifolds
Total absolute curvature of curves in Lorentz Manifolds
Totally real submanifolds of a complex space form.
Totally real surfaces in with parallel mean curvature vector.
Totally Umbilical Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold
2000 Mathematics Subject Classification: 53C40, 53B25.In the present note we study totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold. We have obtained a classification theorem for totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold.
Totally umbilical submanifolds in some semi-Riemannian manifolds
We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.
Trace decomposition and recurrency
Traceless cubic forms on statistical manifolds and Tchebychev geometry
Geometry of traceless cubic forms is studied. It is shown that the traceless part of the cubic form on a statistical manifold determines a conformal-projective equivalence class of statistical manifolds. This conformal-projective equivalence on statistical manifolds is a natural generalization of conformal equivalence on Riemannian manifolds. As an application, Tchebychev type immersions in centroaffine immersions of codimension two are studied.
Translation surfaces of finite type in
In the homogeneous space Sol, a translation surface is parametrized by , where and are curves contained in coordinate planes. In this article, we study translation invariant surfaces in , which has finite type immersion.
Transversally symmetric immersions
We introduce the notions of (extrinsic) locally transversally symmetric immersions and submanifolds in a Riemannian manifold equipped with a unit Killing vector field as analogues of those of (extrinsic) locally symmetric immersions and submanifolds. We treat their geometric properties, derive several characterizations and give a list of examples.