-projective symmetries of fibered manifolds
We prove that the set of the -projective symmetries is a Lie algebra.
Vadim Knizhnik [obituary]
Valeurs propres immergées dans le spectre continu d'une surface de Riemann
Values of pseudoriemannian sectional cuvature.
Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold
The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are -Einstein manifolds of type . Furthermore, we have determined...
Vanishing of the first reduced cohomology with values in an -representation
We prove that the first reduced cohomology with values in a mixing -representation, , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes. We also...
Vanishing Theorems and Almost Symmetrie Spaces of Non-Compact Type.
Vanishing theorems for compact hessian manifolds
A manifold is said to be Hessian if it admits a flat affine connection and a Riemannian metric such that where is a local function. We study cohomology for Hessian manifolds, and prove a duality theorem and vanishing theorems.
Vanishing theorems for Killing vector fields on complete hypersurfaces in the hyperbolic space
We study vanishing theorems for Killing vector fields on complete stable hypersurfaces in a hyperbolic space . We derive vanishing theorems for Killing vector fields with bounded L²-norm in terms of the bottom of the spectrum of the Laplace operator.
Vanishing theorems for the basic cohomology of Riemannian foliations.
Vanishing theorems for twistor spaces
Vanishing theorems on cohomology associated to hermitian symmetric spaces
We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.
Variants on Alexandrov reflection principle and other applications of maximum principle
Variation of geometric invariant theory quotients
Variational calculus on sub-Riemannian manifolds.
Variational equations along integral curves of a projectable system of vector fields
Variational metrics on and the geometry of nonconservative mechanics
Variational principle for the Finslerian extension of general relativity.
Variational principles and symmetries on fibered multisymplectic manifolds
The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special...
Variational problems and PDEs in affine differential geometry
This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss variational problems in equiaffine differential geometry, centroaffine differential geometry and relative differential geometry, which have been studied by Blaschke [Bla], Chern [Ch], C. P. Wang [W], Li-Li-Simon [LLS], and Calabi [Ca-II]. We first derive the Euler-Lagrange equations in these settings; these equations are complicated, strongly nonlinear fourth order PDEs. We...