We use the terms, knot product and local-move, as defined in text of this paper. Let [Formula: see text] be an integer text]. set simple spherical text]-knots prove that map is bijective, where text]Hopf, Hopf denotes link. 1-links Suppose obtained from by a single pass-move, which local-move on 1-links. positive integer. denote following: The text]-dimensional submanifold text]-pass-move, text...

1. Statement of the main results. It will be convenient for us to define an n-knot to be a smooth, connected, oriented, n-dimensional (closed) submanifold IP of S (oriented). If X" is homeomorphic to S, then we call it a spherical knot. All manifolds in this note will be oriented and all constructions we consider will induce canonical orientations. This will be understood and not commented upon...

we obtain the expression of ricci tensor for a $gcr$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $gcr$-lightlike submanifold of anindefinite complex space form. moreover, we have proved that everyproper totally umbilical $gcr$-lightlike submanifold of anindefinite kaehler manifold is a totally geodesic $gcr$-lightlikesubmanifold.

We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.

Let M be a smooth and oriented real submanifold of some n-complex manifold X, of dimension 2m+ 1. A natural question occurs, whether M is the boundary of an (m + 1)-complex submanifold of X. This problem, called the boundary problem, has been extensively treated over the past fifty years when M is compact. The case m = 0, in X = C, has been first solved by Wermer [W] in 1958. Later on, in 1975,...

‎In this paper we study the dynamics of the 2D-motion of a particle of monolayer‎. First we consider the usual physical time component and the plan manifold R2, having the polar coordinates. Then a geometric approach to nonholonomic constrained mechanical systems is applied to a problem from the two dimensional geometric dynamics of the Langmuir-Blodgett monolayer‎. We consider a constraint sub...

we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...

The purpose of this note is to establish the following theorem: Let N be a Kahler manifold, L be an oriented immersed minimal Lagrangian submanifold of N without boundary and V be a holomorphic vector field in a neighbourhood of L in N . Let div(V ) be the (complex) divergence of V . Then the integral ∫ L div(V ) = 0. Vice versa suppose that N is Kahler-Einstein with non-zero scalar curvature a...