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Publications Influence

The Geometry of Walker Manifolds

- M. Brozos-Vázquez, E. García-Río, P. Gilkey, S. Nikcevic, R. Vázquez-Lorenzo
- Mathematics, Computer Science
- The Geometry of Walker Manifolds
- 1 June 2009

TLDR

83 6- PDF

Universal curvature identities

- P. Gilkey, J. H. Park, K. Sekigawa
- Mathematics
- 11 April 2011

Abstract We study scalar and symmetric 2-form valued universal curvature identities. We use this to establish the Gauss–Bonnet theorem using heat equation methods, to give a new proof of a result of… Expand

21 3- PDF

Applications of Affine and Weyl Geometry

- E. García-Río, P. Gilkey, S. Nikcevic, R. Vázquez-Lorenzo
- Computer Science, Mathematics
- Applications of Affine and Weyl Geometry
- 30 May 2013

TLDR

6 3- PDF

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

TLDR

14 2- PDF

Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons

- M. Brozos-Vázquez, E. García-Río, P. Gilkey
- Mathematics
- 17 December 2015

The homogeneous affine surfaces have been classified by Opozda. They may be grouped into 3 families, which are not disjoint. The connections which arise as the Levi-Civita connection of a surface… Expand

23 2- PDF

GEOMETRIC REALIZATIONS OF KAEHLER AND OF PARA-KAEHLER CURVATURE MODELS

- M. Brozos-Vázquez, P. Gilkey, E. Merino
- Mathematics
- 18 September 2009

We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor… Expand

12 1- PDF

Geometric realizations of Hermitian curvature models

- M. Brozos-Vázquez, P. Gilkey, H. Kang, S. Nikcevic
- Mathematics
- 15 December 2008

We show that a Hermitian algebraic curvature model satisfies the Gray identity if and only if it is geometrically realizable by a Hermitian manifold. Furthermore, such a curvature model can in fact… Expand

8 1- PDF

Curvature homogeneous signature (2,2) manifolds

- C. Dunn, P. Gilkey, S. Nikcevic
- Mathematics, Physics
- 23 August 2004

We exhibit a family of generalized plane wave manifolds of signature (2,2). The geodesics in these manifolds extend for infinite time (i.e. they are complete), they are spacelike and timelike Jordan… Expand

12 1- PDF

Conformally Osserman manifolds and self-duality in Riemannian geometry

We study the spectral geometry of the conformal Jacobi operator on a 4-dimensional Riemannian manifold (M,g). We show that (M,g) is conformally Osserman if and only if (M,g) is self-dual or anti… Expand

16 1- PDF

Geometric Realizations of Curvature

- M. Brozos-Vázquez, P. Gilkey, S. Nikcevic
- Mathematics
- 7 April 2009

Introduction and Statement of Results Representation Theory Connections, Curvature, and Differential Geometry Affine Geometry Kahler and Para-Kahler Geometry Affine Geometry Riemannian Geometry… Expand

15 1- PDF