We study the deformation theory of CR maps in positive codimensional case. In particular, we structural properties {\em mapping locus} $E$ (germs nondegenerate) holomorphic $H \colon (M,p) \to M'$ between generic real submanifolds $M \subset \mathbb C^N$ and $M' C^{N'}$, defined to be set points $p' \in which admit such a map with $H(p) = p'$. show that this is semi-analytic provide examples fo...

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite pa...

It is well known that the sphere $S^6(1)$ admits an almost complex structure $J$ which nearly K\"{a}hler. A submanifold $M$ of Hermitian manifold called a CR if it differentiable distribution $\mathcal{D}_1$ such its orthogonal complement totally real distribution. In this case normal bundle also splits into two distributions $\mathcal{D}_3$, complex, and complement. proper three-dimensional si...

we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...