scholarly journals Complete surfaces with negative extrinsic curvature in M2×R

2015 ◽  
Vol 423 (1) ◽  
pp. 538-546
Author(s):  
José A. Gálvez ◽  
José L. Teruel
Keyword(s):  
Extrinsic Curvature ◽  
Complete Surfaces

scholarly journals Weingarten Type Surfaces in ℍ2 × ℝ and 𝕊2 × ℝ

2017 ◽  
Vol 69 (6) ◽  
pp. 1292-1311
Author(s):  
Abigail Folha ◽  
Carlos Peñafiel
Keyword(s):  
Extrinsic Curvature ◽  
Product Spaces ◽  
Intrinsic Curvature ◽  
Complete Surfaces

AbstractIn this article, we study complete surfaces Σ, isometrically immersed in the product spaces ℍ2 × ℝ or 𝕊2 × ℝ having positive extrinsic curvature Ke . Let Ki denote the intrinsic curvature of Σ. Assume that the equation aKi + bKe = c holds for some real constants a ≠ 0,b >0, and c. The main result of this article states that when such a surface is a topological sphere, it is rotational.

scholarly journals Complete surfaces with non-positive extrinsic curvature in H3 and S3

2015 ◽  
Vol 430 (2) ◽  
pp. 1058-1064 ◽  
Author(s):  
José A. Gálvez ◽  
Antonio Martínez ◽  
José L. Teruel
Keyword(s):  
Extrinsic Curvature ◽  
Complete Surfaces

scholarly journals Complete surfaces with positive extrinsic curvature in product spaces

2009 ◽  
pp. 351-386 ◽  
Author(s):  
José Espinar ◽  
José Gálvez ◽  
Harold Rosenberg
Keyword(s):  
Extrinsic Curvature ◽  
Product Spaces ◽  
Complete Surfaces

scholarly journals HIGHER-ORDER CURVATURE TERMS IN BORN–INFELD TYPE BRANE THEORIES

2011 ◽  
Vol 20 (01) ◽  
pp. 59-75 ◽  
Author(s):  
EFRAIN ROJAS
Keyword(s):  
Ricci Tensor ◽  
General Structure ◽  
Extrinsic Curvature ◽  
Higher Order ◽  
Square Root ◽  
Auxiliary Variables ◽  
Field Equations ◽  
Alternative Description ◽  
Brane Models ◽  
Combined Matrix

The field equations associated to Born–Infeld type brane theories are studied by using auxiliary variables. This approach hinges on the fact, that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born–Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending on gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher-order curvature terms appearing in the determinant form come to play in competition with other effective brane models. Additionally, we suggest a Born–Infeld–Einstein type action for branes where the higher-order curvature content is provided by the worldvolume Ricci tensor. This action provides an alternative description of the dynamics of braneworld scenarios.

COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS

2002 ◽  
Vol 17 (20) ◽  
pp. 2762-2762
Author(s):  
E. GOURGOULHON ◽  
J. NOVAK
Keyword(s):  
Numerical Simulations ◽  
Extrinsic Curvature ◽  
Einstein Equations ◽  
Numerical Implementation ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Tensor Density ◽  
Dirac Gauge ◽  
Ill Posed ◽  
Isolated Systems

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

scholarly journals ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR

2002 ◽  
Vol 13 (05) ◽  
pp. 533-548 ◽  
Author(s):  
NICOLAS GINOUX ◽  
BERTRAND MOREL
Keyword(s):  
Dirac Operator ◽  
Lower Bounds ◽  
Dirac Operators ◽  
Extrinsic Curvature ◽  
Eigenvalue Estimates ◽  
Killing Spinors ◽  
Spinor Fields ◽  
Twisted Dirac Operators

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.

scholarly journals Some properties of Grauert type surfaces

2017 ◽  
Vol 28 (08) ◽  
pp. 1750063 ◽  
Author(s):  
Samuele Mongodi ◽  
Zbigniew Slodkowski ◽  
Giuseppe Tomassini
Keyword(s):  
Convex Space ◽  
Level Sets ◽  
Double Cover ◽  
Classification Theorem ◽  
Stein Space ◽  
Pluriharmonic Function ◽  
Exhaustion Function ◽  
Real Analytic ◽  
Complete Surfaces

In a previous work, we classified weakly complete surfaces which admit a real analytic plurisubharmonic exhaustion function; we showed that, if they are not proper over a Stein space, then they admit a pluriharmonic function, with compact Levi-flat level sets foliated with dense complex leaves. We called these Grauert type surfaces. In this note, we investigate some properties of these surfaces. Namely, we prove that the only compact curves that can be contained in them are negative in the sense of Grauert and that the level sets of the pluriharmonic function are connected, thus completing the analogy with the Cartan–Remmert reduction of a holomorphically convex space. Moreover, in our classification theorem, we had to pass to a double cover to produce the pluriharmonic function; the last part of the present paper is devoted to the construction of an example where passing to a double cover cannot be avoided.

scholarly journals Chern–Osserman type equality for complete surfaces inRn

2018 ◽  
Vol 129 ◽  
pp. 117-124
Author(s):  
Qing Chen ◽  
Wenjie Yang
Keyword(s):  
Complete Surfaces

Anomalies generated by extrinsic curvature

1987 ◽  
Vol 36 (3) ◽  
pp. 479-486 ◽  
Author(s):  
F. Langouche ◽  
H. Leutwyler
Keyword(s):  
Extrinsic Curvature
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