Search results for "Differential geometry"

Gibbs and harmonic measures for foliations with negatively curved leaves

2013

In this thesis we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact and negatively curved basis. We also develop a notion of F-harmonic measure and prove that there exists a natural bijective correspondence between the two. For projective foliated bundles with sphere-fibers without transverse invariant measure, we show the uniqueness of these measures for any Hölder potential on the basis. In that case we also prove that F-harmonic measures are realized as weighted limits of large balls tangent to the leaves and that their conditional measures on the fibers are limits of weighted averages on the orbits of the holonomy group.

Integral curves of derivations

1988

We integrate, by a constructive method, derivations of even degree on the sections of an exterior bundle by families of Z 2-graded algebra automorphisms, dependent on a real parameter, and which satisfy a flow condition. We also study the case of local endomorphisms when their components of degree zero and derivations and with no component of negative degree, but then we have integral families of R-linear automorphisms. This integration method can be applied to the Frolicher—Nijenhuis derivations on the Cartan algebra of differential forms, and to the integration of superfields on graded manifolds.

Affine varieties and lie algebras of vector fields

1993

In this article, we associate to affine algebraic or local analytic varieties their tangent algebra. This is the Lie algebra of all vector fields on the ambient space which are tangent to the variety. Properties of the relation between varieties and tangent algebras are studied. Being the tangent algebra of some variety is shown to be equivalent to a purely Lie algebra theoretic property of subalgebras of the Lie algebra of all vector fields on the ambient space. This allows to prove that the isomorphism type of the variety is determinde by its tangent algebra.

The Influence of the Electric Field on the Development of the Swirling Flame Velocity Field and Combustion Characteristics

2008

Gauss maps on canal hypersurfaces of generic curves in R4

2021

Abstract We analyze the generic behavior of the Gauss map in a special case provided by the canal 3-manifolds of curves generically immersed in R 4 and obtain geometrical characterizations for its singularities. We also study the geometrical properties of their corresponding parabolic surfaces, considered as surfaces immersed in R 4 .

Harmonicity and minimality of oriented distributions

2004

We consider an oriented distribution as a section of the corresponding Grassmann bundle and, by computing the tension of this map for conveniently chosen metrics, we obtain the conditions which the distribution must satisfy in order to be critical for the functionals related to the volume or the energy of the map. We show that the three-dimensional distribution ofS4m+3 tangent to the quaternionic Hopf fibration defines a harmonic map and a minimal immersion and we extend these results to more general situations coming from 3-Sasakian and quaternionic geometry.

The geometry of corank 1 surfaces in ℝ4

2018

Abstract We study the geometry of surfaces in ℝ4 with corank 1 singularities. For such surfaces, the singularities are isolated and, at each point, we define the curvature parabola in the normal space. This curve codifies all the second-order information of the surface. Also, using this curve, we define asymptotic and binormal directions, the umbilic curvature and study the flat geometry of the surface. It is shown that we can associate to this singular surface a regular one in ℝ4 and relate their geometry.

Real quadrics in C n , complex manifolds and convex polytopes

2006

In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics Cn which are invariant with respect to the natural action of the real torus (S1)n onto Cn. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-cros…

On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form

1996

We give a nonimmersibility theorem of a compact manifold with nonnegative scalar curvature bounded from above into a geodesic ball of a simply connected space form.

Relativistic simultaneity and causality

2005

We analyze two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity (also known as observed simultaneity), given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that horismos submanifolds are always lightlike. Finally, we establish some conditions to guarantee the existence of foliations in the space-time whose leaves are these submanifolds of simultaneity generated by an observer.