Results 91 to 100 of about 3,198,197 (181)

Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates

Advanced Nonlinear Studies
On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered in (M. Rumin, “Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie ...
Baldi Annalisa, Tripaldi Francesca
doaj   +1 more source

Geometrical aspects of spinor and twistor analysis [PDF]

This work is concerned with two examples of the interactions between differential geometry and analysis, both related to spinors. The first example is the Dirac operator on conformal spin manifolds with boundary.
Calderbank, David M. J.
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Riemannian Maps From Almost Hermitian Manifolds

, 2017
In this chapter, we study Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. In section 1, we study holomorphic Riemannian maps as a generalization of holomorphic submersions and obtain a characterization of such maps. In section 2,
Sahin, Bayram, Bayram Şahin
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Quadratures of Pontryagin extremals for optimal control problems [PDF]

, 2006
We obtain a method to compute effective first integrals by combining Noether's principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls taking values
Rocha, E. A., Rocha, E.A.M., Torres, D. F., Torres, D.F.M.   +3 more
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Holonomy and submanifold geometry [PDF]

, 2002
We survey applications of holonomic methods to the study of submanifold geometry, showing the consequences of some sort of extrinsic version of de Rham decomposition and Berger's Theorem, the so-called Normal Holonomy Theorem.
CONSOLE S, Console, S., Olmos, C., Di Scala, Antonio Jose', OLMOS C.   +4 more
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The Contact Geometry of Sub-Riemannian Structures

Sub-Riemannian geometry, a field that has gained significant traction since the late 20th century, investigates differentiable manifolds endowed with a sub-bundle of the tangent space and a Riemannian metric defined solely on this sub-bundle. This structure, arising naturally in control theory, robotics, and mathematical physics, leads to fascinating ...
Revista, Zen, MATH, 10
openaire   +2 more sources

Connections and Curvature in sub-Riemannian geometry

, 2009
For a subRiemannian manifold and a given Riemannian extension of the metric, we define a canonical global connection. This connection coincides with both the Levi-Civita connection on Riemannian manifolds and the Tanaka-Webster connection on strictly pseudoconvex CR manifolds.
openaire   +2 more sources

The Sub-Riemannian Geometry of Contact Manifolds

This paper explores the intricate relationship between sub-Riemannian geometry and contact manifolds, two fundamental areas of modern differential geometry with profound implications in fields ranging from optimal control theory to theoretical physics. Sub-Riemannian geometry, characterized by a metric defined on a non-integrable distribution, provides
Revista, Zen, MATH, 10
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Dilatation structures in sub-riemannian geometry

, 2007
Based on the notion of dilatation structure arXiv:math/0608536, we give an intrinsic treatment to sub-riemannian geometry, started in the paper arXiv:0706.3644 . Here we prove that regular sub-riemannian manifolds admit dilatation structures. From the existence of normal frames proved by Bellaiche we deduce the rest of the properties of regular sub ...
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On area comparison and rigidity involving the scalar curvature [PDF]

In this thesis we study the effects of lower bounds for the curvature of a Riemannian manifold M on the geometry and topology of closed, minimal hypersurfaces.
Moraru, Vlad
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