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On the composition structure of the twisted Verma modules for $𝔰𝔩 (3, ℂ)$

Libor Křižka, Petr Somberg (2015)

Archivum Mathematicum

We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra $𝔰𝔩 (3, ℂ)$ , including the explicit structure of singular vectors for both $𝔰𝔩 (3, ℂ)$ and one of its Lie subalgebras $𝔰𝔩 (2, ℂ)$ , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as $D$ -modules on the Schubert cells in the full flag manifold for $SL (3, ℂ)$ .

On the concircular curvature tensor of a $(κ, μ)$ -manifold.

Tripathi, Mukut Mani, Kim, Jeong-Sik (2004)

Balkan Journal of Geometry and its Applications (BJGA)

On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay.

Gang Tian, Jeff Cheeger (1994)

Inventiones mathematicae

On the Conformal and CR Automorphism Groups.

R. Schoen (1995)

Geometric and functional analysis

On the conformal relation between twistors and Killing spinors

Friedrich, Thomas (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The author considers the conformal relation between twistors and spinors on a Riemannian spin manifold of dimension $n \geq 3$ . A first integral is constructed for a twistor spinor and various geometric properties of the spin manifold are deduced. The notions of a conformal deformation and a Killing spinor are considered and such a deformation of a twistor spinor into a Killing spinor and conditions for the equivalence of these quantities is indicated.

On the conformal theory of Ichijyō manifolds

Szakál, Sz. (2002)

Proceedings of the 21st Winter School "Geometry and Physics"

Some special linear connection introduced in the Finsler space by Ichijyō has the property that the curvature tensors under conformal changes remain invariant. Two Ichijyō manifolds $(M, E, \nabla)$ and $(M, \bar{E}, \bar{\nabla})$ are said to be conformally equivalent if $\bar{E} = (exp σ^{v}) E$ , $σ \in C^{\infty} (M)$ .It is proved, that in this case, the following assertions are equivalent: 1. $σ$ is constant, 2. $h_{\nabla} = h_{\bar{\nabla}}$ , 3. $S_{\nabla} = S_{\bar{\nabla}}$ , 4. $t_{\nabla} = t_{\bar{\nabla}}$ .It is also proved (when the above conditions are satisfied) that1. If $(M, E, \nabla)$ is a generalized Berwald manifold, then $(M, \bar{E}, \bar{\nabla})$ is also a generalized Berwald manifold.2....