We consider the theory of four-fermion interactions with N-component fermions in de Sitter space. It is found that the effective potential for a composite operator in the theory is calculable in the leading order of the 1/N expansion. The resulting effective potential is analyzed by varying both the four-fermion coupling constant and the curvature of the space-time. The critical curvature at wh...

It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...

The Lemaître-Tolman-Bondi (LTB) model represents an inhomogeneous spherically symmetric universefilledwithfreelyfallingdustlikematterwithoutpressure. First,wehaveconsideredaFinslerian anstaz of (LTB) and have found a Finslerian exact solution of vacuum field equation. We have obtained the R(t,r) and S(t,r) with considering establish a new solution of Rµν = 0. Moreover, we attempttouseFinslergeo...

Neurons in primate inferotemporal cortex (IT) are clustered into patches of shared image preferences. Functional imaging has shown that these patches are activated by natural categories (e.g., faces, body parts, and places), artificial categories (numerals, words) and geometric features (curvature and real-world size). These domains develop in the same cortical locations across monkeys and huma...

In this paper we consider pseudo projectively flat Riemannian manifold whose Ricci tensor S satisfies the condition S(X,Y ) = rT (X)T (Y ), where r is the scalar curvature, T is a non-zero 1-form defined by g(X, ξ) = T (X), ξ is a unit vector field and prove that the manifold is of pseudo quasi constant curvature, integral curves of the vector field ξ are geodesic and ξ is a proper concircular ...

Received We present a model for an inhomogeneous and anisotropic early universe filled with a nonlinear electromagnetic field of Born-Infeld (BI) type. The effects of the BI field are compared with the linear case (Maxwell). Since the curvature invaria nts are well behaved then we conjecture that our model does not present an initial big bang singularity. The existence of the BI field modifies ...

This paper discusses the Norden golden manifold having a constant sectional curvature. First, it is shown that if has real curvature, flat. For this reason, notions of holomorphic-like curvature and bisectional on are investigated, but seen these do not work manifold. shows need for new concept In direction, notion (Norden curvature) proposed, an example given, constant, tensor field expressed ...

An exact four-dimensional black hole solution of gravity with a minimally coupled self-interacting scalar field is reported. The event horizon is a surface of negative constant curvature enclosing the curvature singularity at the origin, and the scalar field is regular everywhere outside the origin. This solution is an asymptotically locally AdS spacetime. The strong energy condition is satisfi...

The present study aimed to characterize the effect of a nearby distractor on vertical, horizontal, and oblique saccade curvature under normal saccade preparation times. Consistent with previous findings, longer-latency vertical saccades showed greater curvature away from a distractor than did oblique or horizontal saccades. At short latencies, vertical saccades also showed greater curvature tow...