Brackets and curvature. (Corchete y curvatura.)
Calculus on symplectic manifolds
On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic form, we find a new complex. In particular, on complex projective space with its Fubini–Study form and connection, we can build a series of differential complexes akin to the Bernstein–Gelfand–Gelfand complexes from parabolic differential geometry.
Canonical forms for -structures in pseudo-riemannian manifolds
Cartan connections and Lie algebroids.
Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of
Center-projective connections
Certain property of the Ricci tensor on Sasakian manifolds
Certain types of affine motion in a Finsler manifold. I
Certain types of affine motion in a Finsler manifold. II
Certain types of affine motion in a Finsler manifold. III
Champs de Yang et Mills variés
Characterization of the Pseudo-symmetries of Ideal Wintgen Submanifolds of Dimension 3
Characterization of totally umbilic hypersurfaces in a space form by circles
In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.
Characterizations of conformally flat hypersurfaces
Chen inequalities for submanifolds of a locally conformal almost cosymplectic manifold with a semi-symmetric metric connection.
Christoffer Symbols and Connection Forms on Infinite-Dimensional Fibre Bundles
Circles and spheres in pseudo-Riemannian geometry.
Classification of -dimensional homogeneous weakly Einstein manifolds
Y. Euh, J. Park and K. Sekigawa were the first authors who defined the concept of a weakly Einstein Riemannian manifold as a modification of that of an Einstein Riemannian manifold. The defining formula is expressed in terms of the Riemannian scalar invariants of degree two. This concept was inspired by that of a super-Einstein manifold introduced earlier by A. Gray and T. J. Willmore in the context of mean-value theorems in Riemannian geometry. The dimension is the most interesting case, where...
Classification of 4-dimensional homogeneous D'Atri spaces
The property of being a D’Atri space (i.e., a space with volume-preserving symmetries) is equivalent to the infinite number of curvature identities called the odd Ledger conditions. In particular, a Riemannian manifold satisfying the first odd Ledger condition is said to be of type . The classification of all 3-dimensional D’Atri spaces is well-known. All of them are locally naturally reductive. The first attempts to classify all 4-dimensional homogeneous D’Atri spaces were done in the papers...
Classification of irreducible holonomies of torsion-free affine connections.