scholarly journals Joinings of higher rank torus actions on homogeneous spaces

2019 ◽  
Vol 129 (1) ◽  
pp. 83-127 ◽  
Author(s):  
Manfred Einsiedler ◽  
Elon Lindenstrauss
Keyword(s):  
Homogeneous Spaces ◽  
Torus Actions ◽  
Higher Rank

scholarly journals Joinings of higher-rank diagonalizable actions on locally homogeneous spaces

2007 ◽  
Vol 138 (2) ◽  
pp. 203-232 ◽  
Author(s):  
Manfred Einsiedler ◽  
Elon Lindenstrauss
Keyword(s):  
Homogeneous Spaces ◽  
Higher Rank ◽  
Locally Homogeneous

HOMOGENEOUS SPACES OF NONPOSITIVE CURVATURE AND THEIR GEODESIC FLOW

1995 ◽  
Vol 06 (02) ◽  
pp. 279-296 ◽  
Author(s):  
JENS HEBER
Keyword(s):  
Homogeneous Space ◽  
Tangent Bundle ◽  
Geodesic Flow ◽  
Homogeneous Spaces ◽  
Nonpositive Curvature ◽  
Partial Classification ◽  
Higher Rank ◽  
Unit Tangent Bundle ◽  
Volume Preserving

Consider the geodesic flow on the unit tangent bundle SH of a 1-connected, irreducible homogeneous space H of nonpositive curvature. We prove that any flow invariant, isometry invariant C0-function on SH is necessarily constant, unless H is symmetric of higher rank. As the main applications, we obtain rigidity and partial classification results for spaces H whose geodesic symmetries are (asymptotically) volume-preserving.

scholarly journals Compact anti-self-dual orbifolds with torus actions

2010 ◽  
Vol 17 (2) ◽  
pp. 223-280 ◽  
Author(s):  
Dominic Wright
Keyword(s):  
Torus Actions

scholarly journals Higher rank Clifford indices of curves on a K3 surface

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Soheyla Feyzbakhsh ◽  
Chunyi Li
Keyword(s):  
Vector Bundles ◽  
Plane Curve ◽  
Smooth Curve ◽  
Line Bundles ◽  
K3 Surface ◽  
Clifford Index ◽  
Smooth Plane ◽  
Higher Rank ◽  
Rank Vector ◽  
Semistable Vector Bundle

AbstractLet (X, H) be a polarized K3 surface with $$\mathrm {Pic}(X) = \mathbb {Z}H$$ Pic ( X ) = Z H , and let $$C\in |H|$$ C ∈ | H | be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when $$g\ge r^2\ge 4$$ g ≥ r 2 ≥ 4 , the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree $$d(\ge 5)$$ d ( ≥ 5 ) smooth plane curve is $$d-4$$ d - 4 , which is the same as the Clifford index of the curve.

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