arXiv math/06087492006-08-30math.DG

Complex Osserman Algebraic Curvature Tensors and Clifford Families

M. Brozos-Vazquez, P. Gilkey

英文摘要：

We classify the algebraic curvature tensors which are both Osserman and complex Osserman in all but a finite number of exceptional dimensions.Information concerning the possible eigenvalue structures, which is provided by methods of algebraic topology, plays a central role in the analysis.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

On quasi-Clifford Osserman curvature tensors

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi-Clifford curvature tensors using a generalized Clifford family and show that they are Osserman. This allows us to discover an Osserman curvature tensor that does not satisfy the duality principle. We give some necessary and some sufficient conditions for the total duality principle.

2019-03-18math.DG

不定内积空间中的Jacobi正交性

The Jacobi-orthogonality in indefinite scalar product spaces

本文推广Jacobi正交性至不定内积空间，研究其与Osserman、Jacobi对偶的关系，证明拟Clifford张量Jacobi正交，并给出3维和4维代数曲率张量Jacobi正交的充要条件。

2023-08-31math.DG

The families Clifford index and differential KO-theory

Extending ideas of Atiyah--Bott--Shapiro and Quillen, we construct a model for differential $\rm KO$-theory whose cocycles are families of Clifford modules with superconnection. The model is built to accommodate an analytic pushforward for bundles of spin manifolds, affording a differential refinement of Atiyah and Singer's families index.

2023-03-16math.ATmath.DG

Determination of the structure of algebraic curvature tensors by means of Young symmetrizers

For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins that every algebraic curvature tensor has a structure which is very similar to that of the above Osserman curvature tensors. We verify our results by means of the Littlewood-Richardson rule and plethysms. For certain symbolic…

2002-12-23cs.SCmath.COmath.DG

旋量表示的显式族

Explicit Families of Spinor Representations

本文提出构建实Clifford代数旋量表示的显式方法，并构造旋量坐标系以计算平行移动，推广至任意符号二次型，证明旋量表示为多向量张量积。

2025-05-22math.DG

Complete curvature homogeneous pseudo-Riemannian manifolds

We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.

2004-04-05math-phmath.DGmath.MP

更多相关论文收起更多论文

Equivariant Chern Weil Forms and The Families Index Theorem

We apply the equivariance --> families principle to a geometric family of Clifford module bundles with an action of a compact Lie group G to prove an equivariant version of Bismut's families index theorem on the differential Borel quotient of the geometric family.

2022-08-10math-phmath.DGmath.MP

Generalized plane wave manifolds

We show that generalized plane wave manifolds are complete, strongly geodesically convex, Osserman, Szabo, and Ivanov-Petrova. We show their holonomy groups are nilpotent and that all the local Weyl scalar invariants of these manifolds vanish. We construct isometry invariants on certain families of these manifolds which are not of Weyl type. Given k, we exhibit manifolds of this type which are k-curvature homogeneous but not locally homogeneous. We also construct a manifold which is weakly 1-curvature homogeneous but not 1-curvature homogeneous.

2005-05-12math-phmath.DGmath.MP

Minimal cubic cones via Clifford algebras

We construct two infinite families of algebraic minimal cones in $R^{n}$. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any $n\ge4$, $n\ne 16k+1$, there is at least one minimal cone in $R^{n}$ given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in $R^{m^2}$, $m\ge2$, defined by an irreducible homogeneous polynomial of degree $…

2010-10-10math.CVmath.DGmath.RA