Generalizations of 3-Sasakian manifolds and skew torsion

DOI10.1515/advgeom-2018-0036zbMath1448.53052arXiv1804.06700OpenAlexW2963797806WikidataQ115156359 ScholiaQ115156359MaRDI QIDQ2194711

Giulia Dileo, Ilka Agricola

Publication date: 7 September 2020

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.06700

zbMATH Keywords

canonical connection3-Sasakian manifoldmetric conecocalibrated \(G_2\)-manifold3-\((\alpha, \delta)\)-Sasaki manifoldalmost 3-contact metric manifoldcanonical almost 3-contact metric manifoldgeneralized Killing spinorKashiwada's theoremmetric connection with skew torsion

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Nilpotent and solvable Lie groups (22E25) Spin and Spin({}^c) geometry (53C27) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Contact manifolds (general theory) (53D10) CR structures, CR operators, and generalizations (32V05) Linear and affine connections (53B05)

Related Items (11)

Odd‐dimensional counterparts of abelian complex and hypercomplex structures ⋮ Curvature properties of \(3\)-\((\alpha ,\delta)\)-Sasaki manifolds ⋮ Invariant spinors on homogeneous spheres ⋮ Homogeneous Sasakian and 3-Sasakian structures from the spinorial viewpoint ⋮ Metric connections with parallel skew-symmetric torsion ⋮ Homogeneous non-degenerate 3-\((\alpha,\delta)\)-Sasaki manifolds and submersions over quaternionic Kähler spaces ⋮ On non-gradient \((m,\rho )\)-quasi-Einstein contact metric manifolds ⋮ Affine connections on 3-Sasakian homogeneous manifolds ⋮ Holonomy and 3-Sasakian homogeneous manifolds versus symplectic triple systems ⋮ Metric connections with parallel twistor-free torsion ⋮ On degenerate 3-\((\alpha, \delta)\)-Sasakian manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariant affine connections on odd-dimensional spheres
• On generalized quasi-Sasaki manifolds
• Twistorial eigenvalue estimates for generalized Dirac operators with torsion
• Quaternionic contact Einstein manifolds
• The odd side of torsion geometry
• 7-dimensional compact Riemannian manifolds with Killing spinors
• Normality of almost contact 3-structure
• Almost contact metric 5-manifolds and connections with torsion
• 3-structures with torsion
• Quaternionic contact structures in dimension 7
• Riemannian almost CR manifolds with torsion
• Spinorial description of \(\mathrm{SU}(3)\)- and \(\mathrm{G}_2\)-manifolds
• Cosymplectic \(p\)-spheres
• 3-quasi-Sasakian manifolds
• A note on flat metric connections with antisymmetric torsion
• Almost contact structures and curvature tensors
• Quaternion Kählerian manifolds
• Remarks on a triple of \(K\)-contact structures
• On nearly parallel \(G_2\)-structures
• On the geometry and classification of absolute parallelisms. II
• Geometry of hyper-Kähler connections with torsion
• Parallel spinors and connections with skew-symmetric torsion in string theory.
• Betti numbers of 3-Sasakian manifolds
• 3-Sasakian manifolds in dimension seven, their spinors and G\(_2\)-structures
• Cones of \(G\) manifolds and Killing spinors with skew torsion
• \(G_2\)-manifolds with parallel characteristic torsion
• 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem
• Hard Lefschetz theorem for Sasakian manifolds
• The existence of special orthonormal frames
• On almost contact 3-structure
• On the geometry and classification of absolute parallelisms. I
• Invariant connections with skew-torsion and $\nabla$-Einstein manifolds
• A deformation of Sasakian structure in the presence of torsion and supergravity solutions
• EINSTEIN MANIFOLDS WITH SKEW TORSION
• REDUCED HOLONOMY, HYPERSURFACES AND EXTENSIONS
• Quaternionic Heisenberg groups as naturally reductive homogeneous spaces
• THE GEOMETRY OF 3-QUASI-SASAKIAN MANIFOLDS
• On manifolds with Sasakian $3$-structure over quaternion Kaehler manifolds
• Riemannian geometry of contact and symplectic manifolds
• On a contact 3-structure

This page was built for publication: Generalizations of 3-Sasakian manifolds and skew torsion