Aspects of Differential Geometry II

Gilkey, Peter Β.; Park, JeongHyeong; Vázquez-Lorenzo, Ramón

doi:10.2200/s00645ed1v01y201505mas016

Cited by 2 publications

(1 citation statement)

References 48 publications

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“…Let H 2 (0, 2) be the hyperbolic plane with a Riemannian metric of constant sectional curvature − 1 4 and let H 2 (1, 1) be the Lorentzian analogue. We recall some facts about the Lie group SL(2, R) and refer to Section 6.8 of Gilkey, Park, and Vázquez-Lorenzo [6] -there are, of course, many excellent references. SL(2, R) is a 3-dimensional Lie group and the Lie algebra sl(2, R) is the vector space of trace free 2 × 2 real matrices.…”

Section: Einstein Geometrymentioning

confidence: 99%

Anti-invariant Riemannian Submersions: A Lie-theoretical Approach

Gilkey¹,

Itoh²,

Park³

2016

Taiwanese J. Math.

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We give a general Lie-theoretic construction for anti-invariant almost Hermitian Riemannian submersions, anti-invariant quaternion Riemannian submersions, anti-invariant para-Hermitian Riemannian submersions, antiinvariant para-quaternion Riemannian submersions, and anti-invariant octonian Riemannian submersions. This yields many compact Einstein examples.2010 Mathematics Subject Classification. 53C15 primary 53B20 and 53C43 secondary. Key words and phrases. Riemannian submersion, anti-invariant almost Hermitian, antiinvariant quaternion, anti-invariant para-Hermitian, anti-invariant para-quaternion, anti-invariant octonian.

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Section: Einstein Geometrymentioning

confidence: 99%

Anti-invariant Riemannian Submersions: A Lie-theoretical Approach

Gilkey¹,

Itoh²,

Park³

2016

Taiwanese J. Math.

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Symmetric affine surfaces with torsion

D'Ascanio

Gilkey

Pisani

2020

Journal of Geometry and Physics

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We study symmetric affine surfaces which have non-vanishing torsion tensor. We give a complete classification of the local geometries possible if the torsion is assumed parallel. This generalizes a previous result of Opozda in the torsion free setting; these geometries are all locally homogeneous. If the torsion is not parallel, we assume the underlying surface is locally homogeneous and provide a complete classification in this setting as well.2010 Mathematics Subject Classification. 53C21.

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Aspects of Differential Geometry II

Cited by 2 publications

References 48 publications

Anti-invariant Riemannian Submersions: A Lie-theoretical Approach

Anti-invariant Riemannian Submersions: A Lie-theoretical Approach

Symmetric affine surfaces with torsion

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