2 citations · 2 across the 11 of their papers we have counts for
11 papers
A New CR Invariant for Contact 3-Manifolds and Classes of Open Books
Ali M. Elgindi
This paper introduces a new CR invariant for co-oriented contact structures on closed, orientable 3-manifolds. The invariant, which we denote as , takes values in the Picar…
New constructions relating Real and Complex Contact Structure
Ali M. Elgindi
We establish new connections between real and complex contact geometry via embeddings of 3-manifolds into $\C^3$. We introduce a new \emph{contact wedge} construction combining two…
Holomorphic Hulls for Compact 3-Manifolds
Ali M. Elgindi
We demonstrate the different possible structures for holomorphic hulls for embeddings of compact real 3-manifolds along the set of complex tangents…
Quantization of Contact 3-Manifolds and the Reeb Gravitational Field
Ali M. Elgindi
We present a canonical geometric quantization scheme for closed contact 3-manifolds using the corresponding explicit embedding $M \hookrightarrow \C^3$ as we constructed in…
Explicit Holomorphic Structures for embeddings of closed 3-manifolds into
Ali M. Elgindi
Expanding on my former work along with the more recent work of Kasuya and Takase, we demonstrate that for a given link which is null-homologous in and for an…
On The Non-Existence of CR-Regular Embeddings of
Ali M. Elgindi
In this article, we show that there exists no CR-regular embedding of the 5-sphere into , and also obtain analogous results for embeddings of higher dimensional…
On the Topological Structure Of Complex Tangencies to Embeddings of into
Ali M. Elgindi
In the mid-1980's, M. Gromov used his machinery of the -principle to prove that there exists totally real embeddings of into . Subsequently, Patrick Ahern an…
Complex Tangencies to Embeddings of Heisenberg Groups and Odd-Dimensional Spheres
Ali M. Elgindi
The notion of a complex tangent arises for embeddings of real manifolds into complex spaces. It is of particular interest when studying embeddings of real -dimensional manifolds…
On the Bishop Invariants of Embeddings of into
Ali M. Elgindi
The Bishop invariant is a powerful tool in the analysis of real submanifolds of complex space that associates to every (non-degenerate) complex tangent of the embedding a non-negat…
A Topological Obstruction to the Removal of a Degenerate Complex Tangent and Some Related Homotopy and Homology Groups
Ali M. Elgindi
In this article, we derive a topological obstruction to the removal of a isolated degenerate complex tangent to an embedding of a 3-manifold into (without affecting…
Totally Real Perturbations and Non-Degenerate Embeddings of
Ali M. Elgindi
In this article, we demonstrate methods for the local removal and modification of complex tangents to embeddings of into . In particular, given any embedding of…