Related papers: Microlocalization and nonexistence of $C^2$ Levi-f…
This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.
This paper has been withdrawn by the author due to a crucial sign error in equation which we use from Ref. 7 that is incorrect. In particular, Eq.(1-8) is not the correct equation from the variation of N. See, for example, Eq.(6) in PRD93,…
We address the problem of existence and uniqueness of a Levi-flat hypersurface $M$ in $C^n$ with prescribed compact boundary $S$ for $n\ge3$. The situation for $n\ge3$ differs sharply from the well studied case $n=2$. We first establish…
This paper has been withdrawn by the author due to a crucial error in formula 4.12.r
In our recent article (to appear in the Journal of Differential Geometry in 2016) we studied tube hypersurfaces in ${\mathbb C}^3$ that are 2-nondegenerate and uniformly Levi degenerate of rank 1. In particular, we discovered that for the…
This paper has been withdrawn by the author due to errors and bad formalization.
We study normal forms of germs of singular real-analytic Levi-flat hypersurfaces. We prove the existence of rigid normal forms for singular Levi-flat hypersurfaces which are defined by the vanishing of the real part of complex…
This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.
This paper has been withdrawn by the author, due to obsolete reference [4], insufficient discussion in sec. 4, and major conceptual error in sec. 5.
This paper has been withdrawn by the author due to an error in the sufficient condition given for the proof of the Tate conjecture for Catanese surfaces.
This paper has been withdrawn by the author due a few mistakes in the paper.
This article has been withdrawn due to an error in a proof of the main result.
The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.
This paper has been withdrawn by the author due to a crucial sign error.
This paper has been withdrawn by the author due to a crucial sign error in equation 1.
This paper has been withdrawn by the authors, due to a crucial error.
This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.
This paper is withdrawn.
This paper has been withdrawn by the author, due to errors in the figures.
We prove the non-existence of real hypersurfaces in CP^2 and CH^2 whose structure Jacobi operator is Lie D-parallel.