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- W4323048049 abstract "Abstract We investigate curvature properties of 3- $$(alpha ,delta )$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -Sasaki manifolds, a special class of almost 3-contact metric manifolds generalizing 3-Sasaki manifolds (corresponding to $$alpha =delta =1$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ) that admit a canonical metric connection with skew torsion and define a Riemannian submersion over a quaternionic Kähler manifold with vanishing, positive or negative scalar curvature, according to $$delta =0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , $$alpha delta >0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>α</mml:mi> <mml:mi>δ</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> or $$alpha delta <0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>α</mml:mi> <mml:mi>δ</mml:mi> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . We shall investigate both the Riemannian curvature and the curvature of the canonical connection, with particular focus on their curvature operators, regarded as symmetric endomorphisms of the space of 2-forms. We describe their spectrum, find distinguished eigenforms, and study the conditions of strongly definite curvature in the sense of Thorpe." @default.
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- W4323048049 date "2023-03-03" @default.
- W4323048049 modified "2023-10-14" @default.
- W4323048049 title "Curvature properties of 3-$$(alpha ,delta )$$-Sasaki manifolds" @default.
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- W4323048049 doi "https://doi.org/10.1007/s10231-023-01310-5" @default.
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