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Our aim is to study the principal bundles determined by the algebra of quaternions in the projective model. The projectivization of the conformal model of the Hopf fibration is considered as example.

The reconstruction theorem $ℳ^{\infty} = ℰ^{\infty} \otimes_{ℰ} ℳ_{r e g}$

J. E. Björk (1981/1982)

Séminaire Équations aux dérivées partielles (Polytechnique)

The Riemann tensor for nonholonomic manifolds.

Leites, Dimitry (2002)

Homology, Homotopy and Applications

The Riemannian curvature tensor and differentiable spaces

Adam Kowalczyk (1984)

Banach Center Publications

The rigidity theorem for Landsberg hypersurfaces of a Minkowski space

Jin Tang Li (2012)

Annales Polonici Mathematici

Let Mⁿ be a compact Landsberg hypersurface of a Minkowski space $(V^{n + 1}, F ̅)$ with constant mean curvature H. Using the Gauss formula for the Chern connection of Finsler submanifolds, we prove that if M is convex, then M is Riemannian with constant curvature.

The $S$ -curvature of homogeneous $(α, β)$ -metrics.

Deng, Shaoqiang, Wang, Xiaoyang (2010)

Balkan Journal of Geometry and its Applications (BJGA)

The Segre imbedding and its converse

Bang-Yen Chen, Wei-Eihn Kuan (1985)

Annales de la Faculté des sciences de Toulouse : Mathématiques

The semiring of immersions of manifolds.

Decruyenaere, F., Dillen, F., Verstraelen, L., Vrancken, L. (1993)

Beiträge zur Algebra und Geometrie

The spectral geometry of the Weyl conformal tensor

N. Blažić, P. Gilkey, S. Nikčević, U. Simon (2005)

Banach Center Publications

We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in the conformal geometry of pseudo-Riemannian manifolds which generalize the Osserman conjecture to this setting. We also study similar questions related to the skew-symmetric curvature operator defined by the Weyl conformal curvature tensor.

The spray and antispray theory in the subspaces of Miron's $O s c^{k} M$ .

Čomić, Irena, Stojanov, Jelena, Grujić, Gabrijela (2008)

Novi Sad Journal of Mathematics

The spread of the shape operator as conformal invariant.

Suceavă, Bogdan D. (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics

Marek Grochowski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we investigate analytic affine control systems $\dot{q}$ q̇ = X + uY, u ∈ [a,b] , where X,Y is an orthonormal frame for a generalized Martinet sub-Lorentzian structure of order k of Hamiltonian type. We construct normal forms for such systems and, among other things, we study the connection between the presence of the singular trajectory starting at q0 on the boundary of the reachable set from q0 with the minimal number of analytic functions needed for describing the reachable set from q0.

The symmetric tensor Lichnerowicz algebra and a novel associative Fourier-Jacobi algebra.

Hallowell, Karl, Waldron, Andrew (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The Tanaka-Webster connection for almost $𝒮$ -manifolds and Cartan geometry

Antonio Lotta, Anna Maria Pastore (2004)

Archivum Mathematicum

We prove that a CR-integrable almost $𝒮$ -manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost $𝒮$ -structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost $𝒮$ -structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal...

The variational principle for the uniform acceleration and quasi-spin in two dimensional space-time.

Matsyuk, Roman Ya. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The volume of geodesic disks in a Riemannian manifold

Oldřich Kowalski, Lieven Vanhecke (1985)

Czechoslovak Mathematical Journal

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