Restrictions of 3-forms in dimension 7 to subspaces of codimension 1
Résultats nouveaux a propos des conjectures de Lichnerowicz et de Carathéodory
R-Geodesics and R-asymptotic lines
Ricci and Bianchi identities for -normal -linear connections on .
Ricci and Casorati principal directions of Chen ideal submanifolds
Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form
We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, -slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.
Ricci curvature and qusiconformal deformations of a Riemannian manifold.
Ricci Curvature of Left Invariant Metrics on Solvable Unimodular Lie Groups.
Ricci curvature of real hypersurfaces in complex hyperbolic space
First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.
Ricci curvature of submanifolds in Kenmotsu space forms.
Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics
By exploiting Perelman’s pseudolocality theorem, we prove a new compactness theorem for Ricci flows. By optimising the theory in the two-dimensional case, and invoking the theory of quasiconformal maps, we establish a new existence theorem which generates a Ricci flow starting at an arbitrary incomplete metric, with Gauss curvature bounded above, on an arbitrary surface. The criterion we assert for well-posedness is that the flow should be complete for all positive times; our discussion of uniqueness...
Ricci flow coupled with harmonic map flow
We investigate a coupled system of the Ricci flow on a closed manifold with the harmonic map flow of a map from to some closed target manifold ,where is a (possibly time-dependent) positive coupling constant. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of a-priori by choosing large enough. Moreover, it suffices to bound the curvature of to also obtain control of ...
Ricci generalized pseudo-parallel Kählerian submanifolds in complex space forms.
Ricci identities in the space of non-symmetric affine connexion
Ricci type identities for basic differentiation and curvature tensors in Otsuki spaces.
Ricci type identities for non-basic differentiation in Otsuki spaces.
Ricci Type Identities In A Subspace Of Space Of Non-Symmetric Affine Connexion
Ricci-flat Kähler metrics on affine algebraic manifolds. II.
Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups
The purpose of this paper is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group , then the restriction of to the center of the Lie algebra of is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group can be...
Ricci-flat metrics on the complexification of a compact rank one symmetric space.