scholarly journals On the Perelman’s reduced entropy and Ricci flat manifolds with maximal volume growth

2012 ◽  
Vol 356 (3) ◽  
pp. 1107-1116 ◽  
Author(s):  
Liang Cheng ◽  
Anqiang Zhu
Keyword(s):  
Volume Growth ◽  
Maximal Volume ◽  
Ricci Flat ◽  
Flat Manifolds

scholarly journals MORE M-BRANES ON PRODUCT OF RICCI-FLAT MANIFOLDS

2012 ◽  
Vol 09 (08) ◽  
pp. 1250067 ◽  
Author(s):  
V. D. IVASHCHUK
Keyword(s):  
Ricci Flat ◽  
Flat Manifolds ◽  
Fractional Numbers

Partially supersymmetric intersecting (non-marginal) composite M-brane solutions defined on the product of Ricci-flat manifolds M0 × M1 × ⋯ × Mn in D = 11 supergravity are considered and formulae for fractional numbers of unbroken supersymmetries are derived for the following configurations of branes: M2 ∩ M2, M2 ∩ M5, M5 ∩ M5 and M2 ∩ M2 ∩ M2. Certain examples of partially supersymmetric configurations are presented.

scholarly journals Stringy tachyonic instabilities of non-supersymmetric Ricci flat backgrounds

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Bobby Samir Acharya ◽  
Gerardo Aldazabal ◽  
Eduardo Andrés ◽  
Anamaría Font ◽  
Kumar Narain ◽  
...  
Keyword(s):  
Small Radius ◽  
Vacuum Energy Density ◽  
Large Radius ◽  
Spin Structures ◽  
Special Holonomy ◽  
Conformal Field ◽  
Ricci Flat ◽  
Flat Manifolds ◽  
Superstring Theories ◽  
M Theory

Abstract Superstring/M-theory compactified on compact Ricci flat manifolds have recently been conjectured to exhibit instabilities whenever the metrics do not have special holonomy. We use worldsheet conformal field theory to investigate instabilities of Type II superstring theories on compact, Ricci flat, spin 3-manifolds including a worldsheet description of their spin structures. The instabilities are signalled by the appearance of stringy tachyons at small radius and a negative (1-loop) vacuum energy density at large radius. We briefly discuss the extension to higher dimensions.

CONSTRUCTION AND PROPERTIES OF QUASI RICCI FLAT SPACES

1986 ◽  
Vol 01 (04) ◽  
pp. 997-1007 ◽  
Author(s):  
GUY BONNEAU ◽  
FRANÇOIS DELDUC
Keyword(s):  
String Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Real ◽  
Ricci Flat ◽  
Compact Case ◽  
Flat Manifolds ◽  
Necessary And Sufficient ◽  
Lagrangian Densities ◽  
Torsion Free

We look for the necessary and sufficient conditions for a generalized torsion-free nonlinear σ-model to be one-loop finite. The corresponding metrics are not only Ricci flat ones, but also a larger class we call “quasi Ricci flat” spaces. We give expressions for the corresponding Lagrangian densities in the real and Kähler cases. In the latter, the manifold is shown to be proper, complete and nonhomogeneous. Unfortunately, in the compact case, relevant for string theory, these quasi Ricci flat manifolds become Ricci flat ones.

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