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De Rham Decomposition for Riemannian Manifolds with Boundary
In this paper, we extend the classical de Rham decomposition theorem to the case of Riemannian manifolds with boundary by using the trick of the...
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HOLONOMY AND 3-SASAKIAN HOMOGENEOUS MANIFOLDS VERSUS SYMPLECTIC TRIPLE SYSTEMS
Our aim is to support the choice of two remarkable connections with torsion in a 3-Sasakian manifold, proving that, in contrast to the Levi-Civita...
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A note on Riemannian connections with skew torsion and the de Rham splitting
We prove that a Riemannian manifold admitting a metric connection with totally skew-symmetric torsion and reducible holonomy is locally reducible,...
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Laplacians and spectrum for singular foliations
The author surveys Connes’ results on the longitudinal Laplace operator along a (regular) foliation and its spectrum, and discusses their...
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Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds
After obtaining an explicit description in coordinates of invariant metrics on four-dimensional non-reductive homogeneous pseudo-Riemannian...
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Lee form and special warped-like product manifolds with locally conformally parallel Spin(7) structure
We study the cases of the Lee form on special warped-like product manifolds M with locally conformally parallel Spin (7) structure to determine the...
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Closed forms and multi-moment maps
We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness...
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Transitive conformal holonomy groups
For ( M , [ g ]) a conformal manifold of signature ( p, q ) and dimension at least three, the conformal holonomy group Hol( M , [ g ]) ⊂ O ( p + 1, q + 1) is an...
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Infinitesimal Isometries Along Curves and Generalized Jacobi Equations
On a Riemannian manifold, a solution of the Killing equation is an infinitesimal isometry. Since the Killing equation is overdetermined,...
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Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature
The holonomy group G of a pseudo-quaternionic-Kählerian manifold of signature (4 r , 4 s ) with non-zero scalar curvature is contained in Sp(1) · Sp( r , s )...
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Multiple almost Einstein structures with intersecting scale singularities
We characterise the S l -doubling construction of Leitner (J Geom Phys 60:1558–1575,
2010 ) by the existence of multiple almost Einstein structures... -
Aspects of conformal holonomy
This is an expository article, which gives an overview about aspects of the theory of conformal holonomy. In particular, we announce a complete...
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New examples of compact manifolds with holonomy Spin(7)
We find new examples of compact Spin(7)-manifolds using a construction of Joyce (J. Differ. Geom., 53:89–130,
1999 ; Compact manifolds with special... -
Half-flat nilmanifolds
We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence...
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Geodesic paths of circles in the plane
Let ℰ be the Fréchet space of all positively oriented embeddings of the circle in ℝ 2 and let ℰ/ ∼ be the quotient of ℰ modulo orientation preserving...
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A holonomy characterisation of Fefferman spaces
We prove that Fefferman spaces, associated to non-degenerate CR structures of hypersurface type, are characterised, up to local conformal isometry,...