اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدFour-dimensional Osserman metrics of neutral signature
125
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jordan Osserman if and only if either it has constant sectional curvature or it is locally a complex space form.
قيم البحث
اقرأ أيضاً
We exhibit Osserman metrics with non-nilpotent Jacobi operators and with non-trivial Jordan normal form in neutral signature (n,n) for any n which is at least 3. These examples admit a natural almost para-Hermitian structure and are semi para-complex
Osserman with non-trivial Jordan normal form as well; they neither satisfy the third Gray identity nor are they integrable.
It is shown that if a compact four-dimensional manifold with metric of neutral signature is Jordan-Osserman, then it is either of constant sectional curvature or Ricci flat.
One says that a smooth manifold M is a pseudo-Riemannian manifold of signature (p,q) if the tangent bundle TM is equipped with a smooth non-degenerate symmetric inner product g of signature (p,q). Similarly one says that M is an affine manifold if TM
is equipped with a torsion free connection. One says g is Osserman if the eigenvalues of the Jacobi operator are constant on the pseudo-sphere bundles of unit timelike and spacelike vectors. We extend this concept from the pseudo-Riemannian to the affine setting to define the notion of a projectively Osserman manifold. This notion is the focus of the paper. We establish some basic results concerning projectively Osserman manifolds and exhibit examples of this structure which arise in several different geometrical contexts.
We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds whi
ch can be written as a twisted product are those of constant curvature.
We derive the Chern-Gauss-Bonnet Theorem for manifolds with smooth non-degenerate boundary in the pseudo-Riemannian context from the corresponding result in the Riemannian setting by examining the Euler-Lagrange equations associated to the Pfaffian o
f a complex metric on the tangent space and then applying analytic continuation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
