We shall prove theorems on nonexistence of certain types of vector fields on a compact manifold with a positive definite Riemannian metric whose Ricci curvature is either everywhere positive or everywhere negative. Actually we shall have some relaxations of the requirements both as to curvature and as to compactness. We shall deal with real spaces with a customary metric and with complex analyt...

a new definition of boundedness of linear order-homomorphisms (loh)in $l$-topological vector spaces is proposed. the new definition iscompared with the previous one given by fang [the continuity offuzzy linear order-homomorphism, j. fuzzy math. 5 (4) (1997)829$-$838]. in addition, the relationship between boundedness andcontinuity of lohs is discussed. finally, a new uniform boundednessprincipl...

The zero-signature Killing metric of a new, real-valued, 8-dimensional gauging of the conformal group accounts for the complex character of quantum mechanics. The new gauge theory gives manifolds which generalize curved, relativistic phase space. The difference in signature between the usual momentum space metric and the Killing metric of the new geometry gives rise to an imaginary proportional...

Let M be an n-dimensional projective algebraic manifold in certain projective space CP . The hyperplane line bundle of CP restricts to an ample line bundle L on M , which is called a polarization of M . A Kähler metric g is called a polarized metric, if the corresponding Kähler form represents the first Chern class c1(L) of L in H (M,Z). Given any polarized Kähler metric g, there is a Hermitian...

Let Nn+p p be an (n + p)-dimensional connected semi-Riemannian manifold of index p. It is called a semi-definite space of index p. When we refer to index p, we mean that there are only p negative eigenvalues of semi-Riemannian metric of Nn+p p and the other eigenvalues are positive. In particular, Nn+1 1 is called a Lorentz space when p = 1. When the Lorentz space Nn+1 1 is of constant curvatur...

‎in this paper we study the existence of fixed points for mappings defined on complete metric spaces‎, ‎satisfying a general contractive inequality depending on two additional mappings‎.

Since its popularization in the 1970s, Fiedler vector of a graph has become standard tool for clustering vertices graph. Recently, Mendel and Noar, Dumitriu Radcliffe, Radcliffe Williamson have introduced geometric generalizations vector. Motivated by questions stemming from their work, we provide structural characterizations when finite metric space can be isometrically embedded Hilbert space.

The study of submanifolds with harmonic mean curvature vector field was initiated by B. Y. Chen in 1985 and arose in the context of his theory of submanifolds of finite type. For a survey on submanifolds of finite type and various related topics was presented in [8, 9]. Let M r be an n-dimensional, connected submanifold of the pseudo-Euclidean space E s . Denote by x⃗, H⃗, and △ respectively the ...

Let V be an n-dimensional vector space over a finite field Fq and P = {1, 2, . . . , n} a poset. We consider on V the poset-metric dP . In this paper, we give a complete description of groups of linear isometries of the metric space (V, dP ), for any poset-metric dP . We show that a linear isometry induces an automorphism of order in poset P , and consequently we show the existence of a pair of...

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...