Anti-invariant Riemannian Submersions: A Lie-theoretical Approach

Abstract

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.

Proper Semi-Slant Pseudo-Riemannian Submersions in Para-Kaehler Geometry

“…A C ∞ −submersion ψ can be defined according to the following conditions. A pseudo-Riemannian submersion ( [4], [15], [21], [22], [34]), an almost Hermitian submersion ( [37], [32], [10]), a slant submersion ( [19], [9], [25], [31]), a para quaternionic submersion ( [5], [16] ), a Clairaut Submersion ( [12]), an anti-invariant submersion ( [11], [13], [30], [8]), anti-invariant Riemnnian submersion from cosymplectic manifolds ( [30], [14]), a quasi-bi-slant Submersion ( [27]), a pointwise slant submersion( [20], [28]), a hemi-slant submersion ( [35], [29]), a semi-invariant submersion ( [23], [33]), a semi-slant ξ ⊥ -Riemannian submersions ( [1], [26]), etc. As we know, Riemannian submersions were severally introduced by B. O'Neill ( [22]) and A.…”

Conformal slant submersions from cosymplectic manifolds

“…Afterwards, he also defined slant submersions from almost Hermitian manifolds in [41]. After that, many geometers studied this area and obtained lots of results on the new topic (see [3,4,6,13,21,25,26,36,38,[44][45][46]). Recent developments on the notion of Riemannian submersion can be found in [43].…”

Conformal slant submersions in contact geometry

“…After that, many geometers study this area and obtain lots of results on the new topic. (see: [3], [4], [5], [14], [21], [24], [25], [36], [37], [43]). Recent developments on the notion of Riemannian submersion could be found in the book, [42].…”