Geometry Associated with Semisimple Flat Homogeneous Spaces

DOI10.2307/1995645zbMath0205.26004OpenAlexW4239209918MaRDI QIDQ5605117

Takushiro Ochiai

Publication date: 1970

Full work available at URL: https://doi.org/10.2307/1995645

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Differential geometry of symmetric spaces (53C35) Differential invariants (local theory), geometric objects (53A55)

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Cites Work

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• The conformal transformation on a space with parallel Ricci tensor
• On the curvature tensor of the hermitian symmetric manifolds
• The infinite groups of Lie and Cartan. I: The transitive groups
• Theory of connections
• On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds
• On the equivalence problems associated with a certain class of homogeneous spaces
• Lie algebra cohomology and the generalized Borel-Weil theorem
• On certain cohomology groups attached to Hermitian symmetric spaces
• On Connections Of Cartan
• Projective Connections and Projective Transformations
• On Automorphisms of A Kählerian Structure
• Conformal Connections and Conformal Transformations
• Characteristic Classes and Homogeneous Spaces, I
• The projective transformation on a space with parallel Ricci tensor
• Transformation Groups on Compact Symmetric Spaces
• Deformation theory of pseudogroup structures
• The Integrability Problem for G-Structures
• Classification of the Finite Nonlinear Primitive Lie Algebras
• On the automorphism group of a G-structure