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Given a fibered manifold $Y \to X$ , a 2-connection on $Y$ means a section $J^{1} Y \to J^{2} Y$ . The authors determine all first order natural operators transforming a 2-connection on $Y$ and a classical linear connection on $X$ into a connection on $J^{1} Y \to Y$ . (The proof implies that there is no first order natural operator transforming 2-connections on $Y$ into connections on $J^{1} Y \to Y$ .) Using this result, the authors deduce several properties of characterizable connections on $J^{1} Y \to X$ .

Some special geometry in dimension six

Čap, Andreas, Eastwood, Michael (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

Motivated by the study of CR-submanifolds of codimension $2$ in $ℂ^{4}$ , the authors consider here a $6$ -dimensional oriented manifold $M$ equipped with a $4$ -dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on $M$ ; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability for these structures....

Some theorems for holomorphic functions with proximate order $1 + l o g (l o g r) / l o g r$

Yoshino, Kunio (1990)

Proceedings of the Winter School "Geometry and Physics"

Space-time decompositions via differential forms

Fecko, Marián (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

The author presents a simple method (by using the standard theory of connections on principle bundles) of $(3 + 1)$ -decomposition of the physical equations written in terms of differential forms on a 4-dimensional spacetime of general relativity, with respect to a general observer. Finally, the author suggests possible applications of such a decomposition to the Maxwell theory.

Special connections on smooth 3-web manifolds

Vanžurová, Alena (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

For a three-web $W$ of codimension $n$ on a differentiable manifold $M^{2 n}$ of dimension $2 n$ , the author studies the Chern connection and a family of parallelizing connections. The latter ones have a common property with the former: the web-distributions are parallel with respect to them.

Special connections on symplectic manifolds

Schwachhöfer, Lorenz J. (2005)

Proceedings of the 24th Winter School "Geometry and Physics"

Special Kaehler manifolds: A survey

Cortés, Vincente (2002)

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

This is a survey of recent contributions to the area of special Kähler geometry. A (pseudo-)Kähler manifold $(M, J, g)$ is a differentiable manifold endowed with a complex structure $J$ and a (pseudo-)Riemannian metric $g$ such that i) $J$ is orthogonal with respect to the metric $g,$ ii) $J$ is parallel with respect to the Levi Civita connection $D .$ A special Kähler manifold $(M, J, g, \nabla)$ is a Kähler manifold $(M, J, g)$ together with a flat torsionfree connection $\nabla$ such that i) $\nabla ω = 0,$ where $ω = g (., J .)$ is the Kähler form and ii) $\nabla$ is symmetric. A holomorphic...

Spectral theory of invariant operators, sharp inequalities, and representation theory

Branson, Thomas (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

The paper represents the lectures given by the author at the 16th Winter School on Geometry and Physics, Srni, Czech Republic, January 13-20, 1996. He develops in an elegant manner the theory of conformal covariants and the theory of functional determinant which is canonically associated to an elliptic operator on a compact pseudo-Riemannian manifold. The presentation is excellently realized with a lot of details, examples and open problems.

Spingroups and spherical means II

Sommen, F. (1987)

Proceedings of the 14th Winter School on Abstract Analysis

Spingroups and spherical means III

Sommen, F. (1989)

Proceedings of the Winter School "Geometry and Physics"

Spinor equations in Weyl geometry

Buchholz, Volker (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

This paper deals with Dirac, twistor and Killing equations on Weyl manifolds with $C$ -spin structures. A conformal Schrödinger-Lichnerowicz formula is presented and used to derive integrability conditions for these equations. It is shown that the only non-closed Weyl manifolds of dimension greater than 3 that admit solutions of the real Killing equation are 4-dimensional and non-compact. Any Weyl manifold of dimension greater than 3, that admits a real Killing spinor has to be Einstein-Weyl.

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