selected scholarly activity
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conferences
- Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions. Oberwolfach Reports. 2529-2568. 2015
- Cohomogeneity one Ricci solitons. AIP Conference Proceedings. 93-98. 2011
- Einstein equations, superpotentials and convex polytopes. Perspectives in Riemannian Geometry. 99-107. 2006
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journal articles
- Linear instability of Sasaki Einstein and nearly parallel G2 manifolds. International Journal of Mathematics. 33. 2022
- Instability of some Riemannian manifolds with real Killing spinors. Communications in Analysis and Geometry. 30:1895-1931. 2022
- Stability of Einstein Metrics on Fiber Bundles. Journal of Geometric Analysis. 31:490-515. 2021
- On the volume of orbifold quotients of symmetric spaces. Differential Geometry and its Application. 71:101639-101639. 2020
- On the linear stability of nearly Kähler 6-manifolds. Annals of Global Analysis and Geometry. 57:15-22. 2020
- Ancient solutions on bundles with non-abelian structural group. Communications in Analysis and Geometry. 28:141-187. 2020
- Ancient solutions of the Ricci flow on bundles. Advances in Mathematics. 318:411-456. 2017
- A Hamiltonian approach to the cohomogeneity one Ricci soliton equations and explicit examples of non-Kähler solitons. Journal of Mathematical Physics. 57. 2016
- Non-Kähler expanding Ricci solitons, Einstein metrics, and exotic cone structures. Pacific Journal of Mathematics. 273:369-394. 2015
- A family of steady Ricci solitons and Ricci-flat metrics. Communications in Analysis and Geometry. 23:611-638. 2015
- Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study. Asian Journal of Mathematics. 17:33-62. 2013
- Classifying superpotentials: Three summands case. Journal of Geometry and Physics. 61:675-692. 2011
- On Ricci solitons of cohomogeneity one. Annals of Global Analysis and Geometry. 39:259-292. 2011
- Non-Kähler Expanding Ricci Solitons. International mathematics research notices. 2009:1107-1133. 2009
- Some New Examples of Non-Kähler Ricci Solitons. Mathematical Research Letters. 16:349-363. 2009
- Classification of Superpotentials. Communications in Mathematical Physics. 284:583-647. 2008
- Superpotentials and the Cohomogeneity One Einstein Equations. Communications in Mathematical Physics. 260:75-115. 2005
- A variational approach for compact homogeneous Einstein manifolds. Geometric and Functional Analysis. 14:681-733. 2004
- On conserved quantities of certain cohomogeneity one Ricci-flat equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 460:1359-1380. 2004
- Painlevé Expansions, Cohomogeneity One Metrics and Exceptional Holonomy. Communications in Analysis and Geometry. 12:887-926. 2004
- Painlevé expansions and the Einstein equations: the two-summand case. Journal of Geometry and Physics. 48:12-43. 2003
- Painlevé analysis of the Ricci-flat ordinary differential equations associated with Aloff–Wallach spaces and U(1)-bundles over Fano products. Journal of Mathematical Physics. 44:3383-3406. 2003
- Integrability and the Einstein equations. Fields Institute Communications. 35:89-101. 2003
- Ricci-flat warped products and Painlevé analysis. Journal of Mathematical Physics. 42:3609-3614. 2001
- The cohomogeneity one Einstein equations and Painlevé analysis. Journal of Geometry and Physics. 38:183-206. 2001
- Einstein metrics from symmetry and bundle constructions. Journal of differential geometry. 6:287-325. 2001
- The initial value problem for cohomogeneity one Einstein metrics. Journal of Geometric Analysis. 10:109-137. 2000
- The cohomogeneity one Einstein equations from the Hamiltonian viewpoint. Journal für die Reine und Angewandte Mathematik. 2000:97-128. 2000
- Integrable Cases of the Einstein Equations. Communications in Mathematical Physics. 208:225-243. 1999
- Kähler-Einstein metrics of cohomogeneity one. Mathematische Annalen. 312:503-526. 1998
- Einstein metrics on $S^{2}$ -bundles. Mathematische Annalen. 310:497-526. 1998
- The ODE System Arising from Cohomogeneity 1 Einstein Metrics. Lecture Notes in Pure and Applied Mathematics. 184:157-165. 1997
- On non-simply connected manifolds with non-trivial parallel spinors. Annals of Global Analysis and Geometry. 13:31-42. 1995
- Metrics with nonnegative isotropic curvature. Duke mathematical journal. 72:649-672. 1993
- Symmetric spaces and strongly isotropy irreducible spaces. Mathematische Annalen. 296:285-326. 1993
- Einstein metrics and quaternionic Kähler manifolds. Mathematische Zeitschrift. 210:305-325. 1992
- On isotropy irreducible Riemannian manifolds. Acta Mathematica. 166:223-261. 1991
- Preserving parallel spinors under metric deformations. Indiana University Mathematics Journal. 40:815-844. 1991
- Einstein metrics on principal torus bundles. Journal of differential geometry. 31:215-248. 1990
- Parallel spinors and parallel forms. Annals of Global Analysis and Geometry. 7:59-68. 1989
- Einstein Metrics with Positive Scalar Curvature. Lecture Notes in Mathematics. 1201:319-336. 1986
- Existence and non-existence of homogeneous Einstein metrics. Inventiones Mathematicae. 84:177-194. 1986
- On normal homogeneous Einstein manifolds. Annales Scientifiques de l'Ecole Normale Supérieure. 18:563-633. 1985
- The isotropy representation of a symmetric space. Rendiconti del Seminario Matematico. Fas Spez:253-261. 1985
- Some remarks on the calculation of Stiefel-Whitney classes and a paper of Wu-Yi Hsiang’s. Pacific Journal of Mathematics. 112:431-443. 1984
- On Actions of Adjoint Type on Complex Stiefel Manifolds. Transactions of the American Mathematical Society. 272:611-611. 1982
- On Actions of Regular Type on Complex Stiefel Manifolds. Transactions of the American Mathematical Society. 272:589-589. 1982
- Some examples of homogeneous Einstein manifolds in dimension seven. Duke mathematical journal. 49:23-28. 1982
- Some Regularity Theorems for Smooth Actions on Complex Stiefel Manifolds. Current Trends in Algebraic Topology, Part 2, Conference Proceedings of Canadian Mathematical Society. 2:303-311. 1982