My research interests are in the area of Differential Geometry:
Einstein metrics, geometry of homogeneous metrics, symmetric
spaces, biquotients, equivariant geometry, and existence of closed
geodesics.
Ggeometry and topology of
cohomogeneity one manifolds, and manifolds with non-negative or positive
sectional curvature.
CV 2021
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pdf file )
Publications
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M.Wang-W.Ziller,
On the isotropy representations of a
symmetric space,
Rend. Sem. Mat. Univ. Politec. Torino , Special Issue, (1983), 253-261.
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pdf file )
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M.Wang-W.Ziller,
On isotropy irreducible Riemannian manifolds,
Acta Math. 166 (1991), 223-261.
(
dvi format )
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D.DeTurck-W.Ziller,
Minimal isometric immersions of spherical space forms in spheres,
Comm. Math. Helv. 67 (1992), 428-458.
(
dvi format )
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M.Wang-W.Ziller,
Symmetric spaces and strongly isotropy irreducible spaces,
Math. Ann. 296 (1993), 285-326.
(
dvi format )
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E.Heintze-W.Ziller,
Isotropy irreducible spaces and s-representations,
Differential Geometry and its Applications 6 (1996) ,
181-188.
(
dvi format )
- W. Ziller,
Weakly symmetric spaces, in Topics in Geometry, Progress in Nonlinear Differential Equations, Vol. 20,
Birkhaeuser 1996, 355-368.
(
dvi format )
- G.Toth-W.Ziller,
Spherical minimal immersions of the 3-sphere,
Comm. Math. Helv. 74 (1999) , 1-34.
(
dvi format )
- K.Grove-W.Ziller, Curvature and Symmetry of Milnor Spheres,
Annals of Mathematics 152 (2000),331-367.
(
dvi format )
- K.Grove-W.Ziller, Cohomogeneity one manifolds with positive Ricci
curvature, Inv. Math. 149 ( 2002),619-649.
pdf file )
- V.Kapovitch-W.Ziller, Biquotients with singly generated rational
cohomology, Geom. Dedicata 104 (2004), 149-160. MINOR CORRECTION ADDED .
( pdf
file )
- C.Boehm-M.Wang-W.Ziller, A variational approach for compact
homogeneous Einstein manifolds, GAFA 14 (2004), 681-733.
( pdf
file ,
Maple file)
- K.Grove-B.Wilking-L.Verdiani-W.Ziller, Non-negative curvature
obstruction in cohomogeneity one and the Kervaire spheres, Ann. del.
Scuola Norm. Sup. 5 (2006), 159-170.
(
pdf file
)
- K.Grove-K.Shankar-W.Ziller, Symmetries of Eschenburg spaces and the
Chern problem, Special Issue in honor of S.S.Chern, Asian J. Math. 10 (2006),
647-662.
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pdf file
)
- T.Chinburg-C.Escher-W.Ziller, Topological properties of Eschenburg
spaces and 3-Sasakian manifolds, Math. Ann. 339 (2007), 3-20. (
pdf file ,
Maple File)
- L.Florit-W.Ziller, Orbifold fibrations of Eschenburg spaces, Geom. Ded. 127
(2007), 159-175.
(
pdf file )
- K.Grove-B.Wilking-W.Ziller, Positively curved cohomogeneity one
manifolds and 3-Sasakian geometry, J. Diff. Geom. 78 (2008), 33-111.
( pdf file )
- L.Florit-W.Ziller, On the topology of positively curved Bazaikin
spaces, J. Europ. Math. Soc. 11 (2009), 189-205.
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pdf file
)
- L.Verdiania-W.Ziller, Positively curved homogeneous metrics on spheres, Math.
Zeitschrift 261 (2009), 473-488.
(
pdf file )
- K.Grove-W.Ziller, Lifting group actions and nonnegative curvature,
Trans. Amer. Math. Soc. 363 (2011) 2865-2890. (
pdf file
)
- K.Grove-L.Verdiani-W.Ziller, An exotic T_1S^4 with positive
curvature, Geom. Funct. Anal. 21 (2011), 499-524. (pdf
file,
Maple file)
- L.Florit-W.Ziller, Topological obstructions to fatness,
Geometry & Topology 15 (2011) 891-925. (
pdf file)
- K.Grove-W.Ziller, Polar manifolds and actions,
J. Fixed Point Theory Appl. 11 (2012), 279-313. (
pdf file)
- L.Verdiani-W.Ziller, Concavity and rigidity in non-negative curvature,
J. Diff. Geom. 97 (2014), 349-375. (
pdf file)
- C.Escher-W.Ziller, Topology of non-negatively curved manifolds,
Annals of Global Analysis and Geometry 46 (2014), 23-55. (
pdf file)
- M.Amann-W.Ziller, Geometrically formal metrics of positive sectional
curvature, Journal of Geometric Analysis 26 (2016), 996-1010. (
pdf file)
- L.Florit-W.Ziller, Nonnegatively curved Euclidean submanifolds in
codimension two, Comm. Math. Helv. 91 (2016), 629-651. (
pdf file)
- M.Xu-W.Ziller, Reversible homogeneous Finsler metrics with positive flag curvature, Forum Math. 29 (2017), 1213-1226. (
pdf file)
- B.Wilking--W.Ziller, Revisiting homogeneous spaces
with positive curvature, Journal fuer
reine und angewandte Mathematik 738 (2018), 313--328. (
pdf file)
- L.Verdiani-W.Ziller, Seven dimensional cohomogeneity one manifolds with nonnegative curvature, Math. Ann. 371 (2018), 655-652. (
pdf file)
- L.Florit-W.Ziller, Manifolds with conullity at most two as graph manifolds, Ann. Scient. de Ec. Norm. Sup. 53 (2020), 1313--1333. (
pdf file)
- R.L.Bryant, P.Foulon, S.Ivanov, V.S.Matveev, W.Ziller, Geodesic behavior for
Finsler metrics of constant positive flag curvature on S^2, J. Diff Geom. 117 (2021), 1--22. (
pdf file)
- L.Verdiani-W.Ziller, Smoothness Conditions in Cohomogeneity one manifolds, Transformation Groups (2020).
(
pdf file)
- T.Buttsworth, A. Pulemotov, Y. Rubinstein, W.Ziller,
The prescribed Ricci curvature problem and the Ricci iteration on homogeneous spheres, Transformation Groups (2021).
(
pdf file)
- L.Florit-W.Ziller, Geometric graph manifolds with non-negative scalar curvvature, to appear in Journal of the London Mathematical Society
(
pdf file)
- L.Verdiani, W.Ziller,
Curvature homogeneous manifolds in dimension 4, J. Geom. Analysis (2021), 8036 -- 8062.
(
pdf file)
- M. Arroyo, A. Pulemotov, W.Ziller,
The prescribed Ricci curvature problem for naturally
reductive metrics on compact Lie groups, Preprint.
(
pdf file)
- M. A. Pulemotov, W.Ziller,
On the varionational properties of the prescribed Ricci curvature functional, Preprint.
(
pdf file)
Surveys
- W.Ziller, Examples of Riemannian manifolds with non-negative sectional
curvature, in: Metric and Comparison Geometry, Surv. Diff. Gem. 11, ed. K.Grove and
J.Cheeger, International Press, 2007, p. 63-102.
(
pdf file )
- W.Ziller, Geometry of positively curved cohomogeneity one manifolds, in:
Riemannian
Topology and Geometric Structures on Manifolds, in honor of Charles Boyer's 65th
birthday, Progress in Mathematics, Birkhaeser, 2008.
(
pdf file )
- W.Ziller, Riemannian manifolds with positive sectional curvature, in:
Geometry of manifolds with non-negative sectional curvature,
ed.
R. Herrera and L. Hernandez-Lamoneda, Lecture Notes in Mathematics, Vol.
2110, 2014. (
pdf file)
- H.Gluck, F.Warner, W.Ziller, Hopf fibrations,
L'Enseignement Mathematique 32 (1986), 173-198. (
pdf file)
Notes
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A survey on Fatness of fiber bundles. This is a preliminary version.
Fatness revisited.
-
A short summary of Eschenburg's Habilitation on biquotients which includes
a Table of his classification of biquotients of equal rank.
Eschenburg Summary
- A complete scanned version of Eschenburg's Habilitation.
Eschenburg Habilitation
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A short summary of Mueter's Ph.D. Thesis on Cheeger deformations.
Mueter Summary
- A complete scanned version of Mueter's Ph.D. thesis.
Mueter Thesis
- A scanned version of Kleiner's Ph.D thesis.
Kleiner thesis