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Conformal/anticonformal actions of the quasi-abelian group $QA_{n}$ of order $2^n$, for $n\geq 4$, on closed Riemann surfaces, pseudo-real Riemann surfaces and closed Klein surfaces are considered. We obtain several consequences, such as…
We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.
In this paper, we investigate properties of orbits of Hermann actions as submanifolds without assuming the commutability of involutions which define Hermann actions. In particular, we compute the second fundamental form of orbits of Hermann…
We construct a one loop amplitude for any Abelian orientifold point group for arbitary complex dimensions. From this we show several results for orientifolds in this general class of models as well as for low dimensional compactifications.…
We outline the construction of invariants of Hamiltonian group actions on symplectic manifolds. These invariants can be viewed as an equivariant version of Gromov-Witten invariants. They are derived from solutions of a PDE involving the…
We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In…
We study the space of closed anti-invariant forms on an almost complex manifold, possibly non compact. We construct families of (non integrable) almost complex structures on $\R^4$, such that the space of closed $J$-anti-invariant forms is…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
In this paper, we prove that full irreducible curvature-adapted isoparametric submanifolds of codimension greater than one in a symmetric space of non-compact type are principal orbits of Hermann actions on the symmetric spaces under…
In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…
In this paper we study a broad class of complete Hamiltonian integrable systems, namely the ones whose associated Lagrangian fibration is complete and has non compact fibres. By studying the associated complete Lagrangian fibration, we show…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
We study when the mapping class group of an infinite-type surface $S$ admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on $S$. We introduce a topological invariant for infinite-type…
The complete invariant for gradient like Morse-Smale dynamical systems (vector fields and diffeomorphisms) on closed 4-manifolds are constructed. It is same as Kirby diagram in a case of polar vector field without fixed points of index 3.
Two geometric inequalities are established for Einstein totally real submanifolds in a complex space form. As immediate applications of these inequalities, some non-existence results are obtained.
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…
Quantum versions of cylindric phase space, like for the motion of a particle on the circle, are obtained through different families of coherent states. The latter are built from various probability distributions of the action variable. The…
We prove existence and regularity of entire solutions to Monge-Ampere equations invariant under an irreducible action of a compact Lie group.