Quarter-pinched Einstein metrics interpolating between real and complex hyperbolic metrics
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-017-2013-x
Abstract: We show that the one-loop quantum deformation of the universal hypermultiplet provides a family of complete 1 / 4-pinched negatively curved quaternionic Kähler (i.e. half conformally flat Einstein) metrics $$g^c$$gc, $$c\ge 0$$c≥0, on $$\mathbb {R}^4$$R4. The metric… read more here.
Keywords: hyperbolic metrics; einstein metrics; hyperbolic; quarter pinched ... See more keywords
Kähler–Einstein metrics and volume minimization
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DOI: 10.1016/j.aim.2018.10.038
Abstract: We prove that if a $\mathbb{Q}$-Fano variety $V$ specially degenerates to a K\"{a}hler-Einstein $\mathbb{Q}$-Fano variety $V$, then for any ample Cartier divisor $H=-r^{-1} K_V$ with $r\in \mathbb{Q}_{>0}$, the normalized volume $\widehat{\rm vol}(v)=A_{\mathcal{C}}^n(v)\cdot {\rm vol}(v)$ is… read more here.
Keywords: einstein metrics; hler einstein; einstein; metrics volume ... See more keywords
On left-invariant Einstein metrics that are not geodesic orbit
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DOI: 10.1016/j.crma.2019.07.003
Abstract: Abstract In this article, we prove that compact simple Lie groups SO ( n ) ( n > 12 ) admit at least two left-invariant Einstein metrics that are not geodesic orbit, which gives a… read more here.
Keywords: geodesic orbit; einstein metrics; invariant einstein; metrics geodesic ... See more keywords
Sasaki–Einstein metrics on a class of 7-manifolds
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DOI: 10.1016/j.geomphys.2019.01.007
Abstract: In this note we give an explicit construction of Sasaki-Einstein metrics on a class of simply connected 7-manifolds with the rational cohomology of the 2-fold connected sum of $S^2\times S^5$. The homotopy types are distinguished… read more here.
Keywords: einstein metrics; sasaki einstein; metrics class; geometry ... See more keywords
Einstein metrics, projective structures and the SU(∞) Toda equation
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DOI: 10.1016/j.geomphys.2019.103523
Abstract: Abstract We establish an explicit correspondence between two-dimensional projective structures admitting a projective vector field, and a class of solutions to the S U ( ∞ ) Toda equation. We give several examples of new,… read more here.
Keywords: metrics projective; toda equation; einstein metrics; projective structures ... See more keywords