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Geometry of compactifications of locally symmetric spaces

Lizhen Ji, Robert Macpherson (2002)

Annales de l’institut Fourier

For a locally symmetric space M , we define a compactification M ∪ M ( ∞ ) which we call the “geodesic compactification”. It is constructed by adding limit points in M ( ∞ ) to certain geodesics in M . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give M ( ∞ ) for locally symmetric spaces. Moreover, M ( ∞ ) has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...

Geometry of control-affine systems.

Clelland, Jeanne N., Moseley, Christopher G., Wilkens, George R. (2009)

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

Geometry of Mus-Sasaki metric

Abderrahim Zagane, Mustapha Djaa (2018)

Communications in Mathematics

In this paper, we introduce the Mus-Sasaki metric on the tangent bundle T M as a new natural metric non-rigid on T M . First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.

Geometry of oblique projections

E. Andruchow, Gustavo Corach, D. Stojanoff (1999)

Studia Mathematica

Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections P a determined by the different involutions a induced by positive invertible elements a ∈ A. The maps φ : P → P a sending p to the unique q ∈ P a with the same range as p and Ω a : P a → P a sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q,r ∈ A with ||q-r|| < 1 such that...

Geometry of second-order connections and ordinary differential equations

Alexandr Vondra (1995)

Mathematica Bohemica

The geometry of second-order systems of ordinary differential equations represented by 2 -connections on the trivial bundle error ℝ × M → ℝ is studied. The formalism used, being completely utilizable within the framework of more general situations (partial equations), turns out to be of interest in confrontation with a traditional approach (semisprays), moreover, it amounts to certain new ideas and results. The paper is aimed at discussion on the interrelations between all types of connections having to do with...

Geometry of some twistor spaces of algebraic dimension one

Nobuhiro Honda (2015)

Complex Manifolds

It is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by...

Geometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold

Atçeken, Mehmet (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 53C42, 53C15.In this article, we have studied warped product semi-invariant submanifolds in a locally Riemannian product manifold and introduced the notions of a warped product semi-invariant submanifold. We have also proved several fundamental properties of a warped product semi-invariant in a locally Riemannian product manifold.Supported by the Scientific Research Fund of St. Kl. Ohridski Sofia University under contract 90/2008.

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