É. Cartan proved that conformally flat hypersurfaces in Sn+1 for n > 3 have at most two distinct principal curvatures and locally envelop a one-parameter family of (n − 1)-spheres. We prove that the Gauss-Codazzi equation for conformally flat hypersurfaces in S4 is a soliton equation, and use a dressing action from soliton theory to construct geometric Ribaucour transforms of these hypersurface...

We introduce and study a special class of Kato manifolds, which we call toric manifolds. Their construction stems from geometry, as their universal covers are open subsets algebraic varieties non-finite type. This generalizes previous constructions Tsuchihashi Oda, in complex dimension 2, retrieves the properly blown-up Inoue surfaces. topological analytical properties manifolds link certain in...

We introduced a class of conformally invariant Ehresmann connections so–called L-horizontal endomorphism in [7]. Using this class, we define conformally invariant manifolds: Wagner–type manifold and locally Minkowski–type manifold as special generalized Berwald manifolds. Then a generalization of Hashiguchi–Ichijyō’s Theorems to Wagner–type manifolds is presented. Mathematics Subject Classifica...

We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.

A differential geometric statement of the noncommutative topological index theorem is worked out for covariant star products on vector bundles. To start, a manifold considered as product space [Formula: see text], wherein text] closed manifold, and flat Calabi–Yau text]-fold. Also, semi-conformally metric which leads to dynamical spacetime from viewpoint gravity. Based Kahler form defined covar...

In this paper, we have proved that if a complete conformally flat gradient shrinking Ricci soliton has linear volume growth or the scalar curvature is finitely integrable and also reciprocal of potential function subharmonic, then manifold isometric to Euclidean sphere. As consequence, showed four dimensional satisfying some conditions $\mathbb{S}^4$ $\mathbb{RP}^4$ $\mathbb{CP}^2$. We deduced ...