pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.

0. Introduction and Preliminary 2 0.1. Existence and uniqueness theorem 2 0.2. Equation of a chain 7 1. Nonsingular matrices 9 1.1. A family of nonsingular matrices 9 1.2. Sufficient condition for Nonsingularity 12 1.3. Estimates 16 2. Local automorphism group of a real hypersurface 23 2.1. Polynomial Identities 23 2.2. Injectivity of a Linear Mapping 33 2.3. Beloshapka-Loboda Theorem 42 3. Com...

In this paper we introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample point for the connected component of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of th...

We study singular real-analytic Levi-flat hypersurfaces in complex projective space. We give necessary and sufficient conditions for such a hypersurface to be a pullback of a real-analytic curve in C via a meromorphic function. We define the rank of a real hypersurface and study the connections between rank, degree, and the type and size of the singularity for Levi-flat hypersurfaces. Finally, ...

let $(m^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the sasakian space form$widetilde{m}(c)$. we show that if the shape operator $a$ of $m$ isrecurrent then it is parallel. moreover, we show that $m$is locally a product of two constant $phi-$sectional curvaturespaces.

We initiate a systematic local study of singular Levi-flat real analytic hypersurfaces, concentrating on the simplest nontrivial case of quadratic singularities. We classify the possible tangent cones to such hypersurfaces and prove the existence and convergence of a rigid normal form in the case of generic (Morse) singularities. We also characterize when such a hypersurface is defined by the v...

We characterize C embedded hypersurfaces of R as the only locally closed sets with continuously varying flat tangent cones whose measuretheoretic-multiplicity is at most m < 3/2. It follows then that any (topological) hypersurface which has flat tangent cones and is supported everywhere by balls of uniform radius is C. In the real analytic case the same conclusion holds under the weakened hypot...