We study the multiplicity mod 2 of real algebraic hypersurfaces. We prove that under some assumptions on the singularity it is preserved through a semi-algebraic bi-Lipschitz homeomorphism of R. In a first part we find a part of the tangent cone enclosing the multiplicity mod 2 and prove that it is an equivariant subset of S. Studying equivariant submanifolds of S we are able to conclude about ...

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We find Ricci curvature bounds for pointwise semi-slant warped products submanifolds in non-Sasakian generalized Sasakian space forms this work, and analyze the equality case of inequality. The derived inequality is also used to develop a number applications.