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Displaying 521 – 540 of 791

On the Finsler geometry of the Heisenberg group $H_{2 n + 1}$ and its extension

Mehri Nasehi (2021)

Archivum Mathematicum

We first classify left invariant Douglas $(α, β)$ -metrics on the Heisenberg group $H_{2 n + 1}$ of dimension $2 n + 1$ and its extension i.e., oscillator group. Then we explicitly give the flag curvature formulas and geodesic vectors for these spaces, when equipped with these metrics. We also explicitly obtain $S$ -curvature formulas of left invariant Randers metrics of Douglas type on these spaces and obtain a comparison on geometry of these spaces, when equipped with left invariant Douglas $(α, β)$ -metrics. More exactly, we show...

On the first Chern class of a complex submanifold in an almost Hermitian manifold and the normal connection

Manuel Barros, Florentino G. Santos (1987)

Colloquium Mathematicae

On the first eigenvalue of spacelike hypersurfaces in Lorentzian space

Bing Ye Wu (2006)

Archivum Mathematicum

In this paper we obtain a lower bound for the first Dirichlet eigenvalue of complete spacelike hypersurfaces in Lorentzian space in terms of mean curvature and the square length of the second fundamental form. This estimate is sharp for totally umbilical hyperbolic spaces in Lorentzian space. We also get a sufficient condition for spacelike hypersurface to have zero first eigenvalue.

On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space.

Robert C. Reilly (1977)

Commentarii mathematici Helvetici

On the first secondary invariant of Molino's central sheaf

Jesús A. Álvarez López (1996)

Annales Polonici Mathematici

For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and other geometric properties are also proved to be equivalent to tautness.

On the Focal Locus of a Submanifold in a Riemannian Manifold of Constant Sectional Curvature

Hukum Singh (1985)

Publications de l'Institut Mathématique

On the four vertex theorem in planes with radial density $e^{φ (r)}$

Doan The Hieu, Tran Le Nam (2008)

Colloquium Mathematicae

It is shown that in a plane with a radial density the four vertex theorem holds for the class of all simple closed curves if and only if the density is constant. On the other hand, for the class of simple closed curves that are invariant under a rotation about the origin, the four vertex theorem holds for every radial density.

On the four-dimensional $T^{2}$ -manifolds of positive Ricci curvature.

Bazajkin, Ya.V., Matvienko, I.V. (2007)

Sibirskij Matematicheskij Zhurnal

On the Fundamental Group of a Visibility Manifold.

V. Schroeder (1986)

Mathematische Zeitschrift

On the Fundamental Group of Non-Positively Curved Manifolds.

Michael T. Anderson (1986)

Mathematische Annalen

On the Gauss curvature of maximal surfaces in the 3-dimensional Lorentz-Minkowski space.

Alfonso Romero, F. J.M. Estudillo (1994)

Commentarii mathematici Helvetici

On the Gauss image of a spacelike hypersurface with constant mean curvature in Minkowski space.

Y.L. Xin (1991)

Commentarii mathematici Helvetici

On the Gauss map of B-scrolls in $3$ -dimensional Lorentzian space forms

Angel Ferrández, Pascual Lucas (2000)

Czechoslovak Mathematical Journal

In this note we show that $B$ -scrolls over null curves in a 3-dimensional Lorentzian space form ${\bar{M}}_{1}^{3} (c)$ are characterized as the only ruled surfaces with null rulings whose Gauss maps $G$ satisfy the condition $Δ G = Λ G$ , $Λ X (\bar{M}) \to X (\bar{M})$ being a parallel endomorphism of $X (\bar{M})$ .

On the Gauss map of complete surfaces of constant mean curvature in R3 and R4.

R. Osserman, R. Schoen, D.A. Hoffman (1982)

Commentarii mathematici Helvetici

On the Gauss-Kronecker Curvature Tensors.

Oldrich Kowalski (1973)

Mathematische Annalen

On the generalized Lagrange spaces associated to the remarkable Lagrangians.

Creţu, Ciprian (1997)

General Mathematics

On the generic spectrum of a riemannian cover

Steven Zelditch (1990)

Annales de l'institut Fourier

Let $M$ be a compact manifold let $G$ be a finite group acting freely on $M$ , and let $ℳ_{G}$ be the (Fréchet) space of $G$ -invariant metric on $M$ . A natural conjecture is that, for a generic metric in $ℳ_{G}$ , all eigenspaces of the Laplacian are irreducible (as orthogonal representations of $G$ ). In physics terminology, no “accidental degeneracies” occur generically. We will prove this conjecture when dim $M \geq$ dim $V$ for all irreducibles $V$ of $G$ . As an application, we construct isospectral manifolds with simple eigenvalue...

Currently displaying 521 – 540 of 791

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Displaying 521 – 540 of 791

On the Finsler geometry of the Heisenberg group $H_{2 n + 1}$ and its extension

On the first Chern class of a complex submanifold in an almost Hermitian manifold and the normal connection

On the first eigenvalue of spacelike hypersurfaces in Lorentzian space

On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space.

On the first secondary invariant of Molino's central sheaf

On the Focal Locus of a Submanifold in a Riemannian Manifold of Constant Sectional Curvature

On the four vertex theorem in planes with radial density $e^{φ (r)}$

On the four-dimensional $T^{2}$ -manifolds of positive Ricci curvature.

On the Fundamental Group of a Visibility Manifold.

On the Fundamental Group of Non-Positively Curved Manifolds.

On the Gauss curvature of maximal surfaces in the 3-dimensional Lorentz-Minkowski space.

On the Gauss image of a spacelike hypersurface with constant mean curvature in Minkowski space.

On the Gauss map of B-scrolls in $3$ -dimensional Lorentzian space forms

On the Gauss map of complete surfaces of constant mean curvature in R3 and R4.

On the Gauss-Kronecker Curvature Tensors.

On the generalized Lagrange spaces associated to the remarkable Lagrangians.

On the generic spectrum of a riemannian cover

On the geodesic connectedeness of Lorentzian manifolds.

On the geodesic connectedness of simply connected Lorentz surfaces

On the geodesic projection of connections

Currently displaying 521 – 540 of 791