A self-similar Hessian (special Kähler) manifold is a $$(M,\nabla ,g)$$ endowed with an affine (holomorphic) homothetic vector field $$\xi $$ . Consider action of group G on ,g,\xi )$$ by isometries preserving such that acts the level set $$\{g(\xi ,\xi )=1\}$$ simply transitively. Then, we construct homogeneous conformally Kähler (hyper structure TM $$(T^*M)$$

Every sequence of positive or negative homothetic copies of a planar convex body C whose total area does not exceed 0.175 times the area of C can be translatively packed in C. Let C be a planar convex body with area |C|. Moreover, let (Ci) be a finite or infinite sequence of homothetic copies of C. We say that (Ci) can be translatively packed in C if there exist translations σi such that σiCi a...

The paper provides an extension and a new proof of Deaton’s theorem on the undesirability of nonuniform excise taxation when income taxes are a¢ ne and preferences over consumption goods are separable from labour-leisure choices, homothetic, and identical across agents. Key Words: Optimal Excise Taxes, Atkinson-Stiglitz Theorem, Deaton’s Theorem JEL Classi…cation: H21

Sets thrown at random in space contain, on average, a number of integer points equal to the measure of these sets. We determine the mean square error in the estimate of this number when the sets are homothetic to a domain with fractal boundary. This is related to the problem of approximating Lebesgue integrals by random Riemann sums.

We define a global horizontal 4-form on a quaternionic contact manifold and show that it is closed if and only if the torsion of the Biquard connection vanishes provided the dimension is grater than seven. This condition characterizes quaternionic contact structures which are locally qc homothetic to 3-sasakian.

We consider the planar three-body problem with generalized potentials. Some nonintegrability results for these systems have been obtained by analyzing variational equations along homothetic solutions. But we cannot apply it to several exceptional cases. For example, in case of inverse-square potentials, solutions are solvable. obtain sufficient conditions cases focusing on some particular that ...