Nonpositivity: Curvature vs. curvature operator

SLED phenomenology: curvature vs. volume

We assess the question whether the SLED (Supersymmetric Large Extra Dimensions) model admits phenomenologically viable solutions with 4D maximal symmetry. We take into account a finite brane width and a scale invariance (SI) breaking dilaton-brane coupling, both of which should be included in a realistic setup. Provided that the brane tension and the microscopic size of the brane take generic v...

Complete Manifolds with Nonnegative Curvature Operator

In this short note, as a simple application of the strong result proved recently by Böhm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of Böhm and Wilking, we show that any complete Riemannian manifold (with dimension ≥ 3) whose curvature operator is bounded and satisfies the pinching condition ...

Landsberg Curvature, S-curvature and Riemann Curvature

Symmetric curvature tensor

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...

Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2

Let R be an algebraic curvature tensor for a non-degenerate inner product of signature (p, q) where q ≥ 5. If π is a spacelike 2 plane, let R(π) be the associated skewsymmetric curvature operator. We classify the algebraic curvature tensors so R(·) has constant rank 2 and show these are geometrically realizable by hypersurfaces in flat spaces. We also classify the Ivanov-Petrova algebraic curva...