75 research outputs found
Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres
In contrast to the homogeneous case, we show that there are compact
cohomogeneity one manifolds, that do not support invariant metrics of
non-negative sectional curvature. In fact we exhibit infinite families of such
manifolds including the exotic Kervaire spheres. Such examples exist for any
codimension of the singular orbits except for the case where both are equal to
two, where existence of non-negatively curved metrics is known.Comment: 10 page
Instantons and Killing spinors
We investigate instantons on manifolds with Killing spinors and their cones.
Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds,
nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and
3-Sasakian manifolds. We construct a connection on the tangent bundle over
these manifolds which solves the instanton equation, and also show that the
instanton equation implies the Yang-Mills equation, despite the presence of
torsion. We then construct instantons on the cones over these manifolds, and
lift them to solutions of heterotic supergravity. Amongst our solutions are new
instantons on even-dimensional Euclidean spaces, as well as the well-known
BPST, quaternionic and octonionic instantons.Comment: 40 pages, 2 figures v2: author email addresses and affiliations adde
The Wide-field Spectroscopic Telescope (WST) Science White Paper
The Wide-field Spectroscopic Telescope (WST) is proposed as a new facility dedicated to the efficient delivery of spectroscopic surveys. This white paper summarises the initial concept as well as the corresponding science cases. WST will feature simultaneous operation of a large field-of-view (3 sq. degree), a high multiplex (20,000) multi-object spectrograph (MOS) and a giant 3x3 sq. arcmin integral field spectrograph (IFS). In scientific capability these requirements place WST far ahead of existing and planned facilities. Given the current investment in deep imaging surveys and noting the diagnostic power of
spectroscopy, WST will fill a crucial gap in astronomical capability and work synergistically with future ground and space-based facilities. This white paper shows that WST can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; origin of stars and planets; time domain and multi-messenger astrophysics. WST's uniquely rich dataset will deliver unforeseen discoveries in many of these areas. The WST Science Team (already including more than 500 scientists worldwide) is open to the all astronomical community. To register in the WST Science Team please visit https://www.wstelescope.com/for-scientists/participat
Complex n-dimensional manifolds with a real n(2)-dimensional automorphism group
The main theorem of this article is a characterization of non compact simply connected complete Kobayashi hyperbolic complex manifold of dimension n >= 2 with real n(2)-dimensional holomorphic automorphism group. Together with the earlier work [11, 12] and [13] of Isaev and Krantz, this yields a complete classification of the simply-connected, complete Kobayashi hyperbolic manifolds with dim(R) Aut (M) >= (dim(C) M)(2).X1112sciescopu
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