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Steven Gindi

Publications and source records attributed to Steven Gindi.

7 recordsLinked to original sources
arXiv2024

Ricci Flows with Nilpotent Symmetry and Zero Bundle Curvature

We use Lott's functional and construct a new functional to derive rigidity results for invariant Ricci flow blowdown limits on nilpotent principal bundles with zero associated curvature. Consequently, we prove that the blowdown limit is locally an expanding Ricci soliton when the structure group is the three dimensional Heisenberg group. In addition, we classify this soliton when the base manifold is one dimensional. This, together with Lott's work in the abelian setting, yields a complete local classification of invariant Ricci flow blowdown limits on four dimensional, nilpotent principal bundles.

math.DG↗
arXiv2021

Four-dimensional generalized Ricci flows with nilpotent symmetry

We study solutions to generalized Ricci flow on four-manifolds with a nilpotent, codimension $1$ symmetry. We show that all such flows are immortal, and satisfy type III curvature and diameter estimates. Using a new kind of monotone energy adapted to this setting, we show that blowdown limits lie in a canonical finite-dimensional family of solutions. The results are new for Ricci flow.

math.DG↗
arXiv2015

Algebroids and Twistor Spaces

We introduce a plethora of skew algebroids on twistor spaces and describe the corresponding foliations. In a forthcoming paper, we use these algebroids to derive results about bihermitian manifolds, also known as generalized Kahler manifolds.

math.DG↗
arXiv2013

Bihermitian Geometry and the Holomorphic Sections of Twistor Space

In this paper, we construct tools from the holomorphic twistor spaces that we introduced in \cite{Gindi1} to derive results about the complex geometries of their base manifolds. In particular, we develop a new approach to studying generalized Kahler manifolds that leads to insights into their real and holomorphic Poisson structures.

math.DG↗
arXiv2012

Integrable Complex Structures on Twistor Spaces

We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case we construct a metric and three compatible complex structures on the twistor space that have equal torsions.

math.DG↗
arXiv2008

Representation Theory of the Algebra Generated By a Pair of Complex Structures

The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to those of the infinite dihedral group, we give the algebra the name iD-infinity.

math.RT↗