On the geometry of four dimensional Riemannian manifold with a circulant metric and a circulant affinor structure
Abstract
We consider a four dimensional Riemannian manifold M with a metric g and an affinor structure q. We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B), A, B, C ∈ FM and (0, 1, 0, 0), respectively. Let ∇ be the connection of g. Further, let mu1, mu2,mu3, mu4, mu5, mu6 be the sectional curvatures of 2-sections x, qx, x, q2x, q3x, x, qx, q2x, qx, q3x, q2x, q3x for arbitrary vector x in TpM$, p is in M . Then we have that q4=E; g(qx, qy)=g(x,y), x, y are in chiM. The main results of the present paper are 1) There exist a q-base in TpM, p is in M. 2) if ∇ q=0, then μ1= μ3=μ4=μ6, μ2= μ5=0.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.