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The orthogonality principle for Osserman manifolds
We introduce a new potential characterization of Osserman algebraic curvature tensors. An algebraic curvature tensor is Jacobi-orthogonal if
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Gravity and Dark Matter in the Framework of Metric-Affine Geometry
In this paper, we generalize space-time manifold by considering metric-affine structure on space-time manifold. Metric-affine geometry is defined in...
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Symmetric, Semisymmetric, and Recurrent Projectively Euclidean Spaces
In this paper, we present some results obtained for symmetric, semisymmetric, and semisymmetric recurrent projectively Euclidean spaces. Components...
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On Prescribed Values of the Operator of Sectional Curvature on Three-Dimensional Locally Homogeneous Lorentzian Manifolds
In this paper, the problem of prescribed values of the operator of sectional curvature on a three-dimensional locally homogeneous Lorentzian...
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On Geodesic Definiteness by Similarity Points
In this paper, we present some results obtained in the theory of geodesic map**s of surfaces. It is well known that a map** that is both...
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Einstein’s Equation on Three-Dimensional Metric Lie Groups with Vector Torsion
In this paper, we study the Einstein equation on three-dimensional Lie groups equipped with a left-invariant (pseudo) Riemannian metric and a metric...
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Geometry of Fibered Graphs of Map**s
In this paper, we examine the differential-geometric aspect of constant-rank map**s of smooth manifolds based on the concept of a graph as a smooth...
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Conformally flat affine hypersurfaces with semi-parallel cubic form
In this paper, we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative...
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Translating Solutions of the Nonparametric Mean Curvature Flow with Nonzero Neumann Boundary Data in Product Manifold Mn × ℝ
In this paper, the authors can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary...
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Conformally flat, minimal, Lagrangian submanifolds in complex space forms
We investigate n -dimensional ( n ⩾ 4), conformally flat, minimal, Lagrangian submanifolds of the n -dimensional complex space form in terms of the...
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Metrics and Connections on the Bundle of Affinor Frames
In this paper the authors consider the bundle of affinor frames over a smooth manifold, define the Sasaki metric on this bundle, and investigate the...
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Metric Affine Spaces
This paper is a review of some directions in the study of special classes of metric affince spaces, i.e., spaces endowed with a (pseudo)Riemannian...
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Curvature Properties of Interior Black Hole Metric
A spacetime is a connected 4-dimensional semi-Riemannian manifold endowed with a metric tensor g with signature (− + ++). The geometry of a spacetime...
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On Riemannian submersions
We prove that the image of a real analytic Riemannian manifold under a smooth Riemannian submersion is necessarily real analytic.
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Spheres and circles in a tangent space of a 4-dimensional Riemannian manifold with respect to an indefinite metric
Our study is in the tangent space at an arbitrary point on a 4-dimensional Riemannian manifold. The manifold is equipped with an additional tensor...
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Minimal Surfaces in Three-Dimensional Riemannian Manifold Associated with a Second-Order ODE
We show that a surface corresponding to a first-order ODE is minimal in three-dimensional Riemannian manifold which is determined by the first...