In this paper we construct a large class of new normal forms for Levi-nondegenerate real hypersurfaces in complex spaces. We adopt a general approach illustrating why these normal forms are natural and which role is played by the celebrated Chern-Moser normal form [CM74]. The latter appears in our class as the one with the ”maximum normalization” in the lowest degree. However, there are other n...

In this paper, warped product CRCR-submanifolds in Kahler manifolds and contact Sasakian, Kenmotsu cosymplectic manifolds, are shown to possess a geometric property; namely DTDT-minimal. Taking benefit from property, an optimal general inequality is established by means of the Gauss equation, we leave cosyplectic because it easy structure. Moreover, rich geometry appears when necessity sufficie...