COMPLEX VARIETIES

Author: CERDÁN SALA ANA ÁFRICA.
Year: 2005.
University: ALICANTE.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: Over history have been studied and shown numerous geometric inequalities. The first to be raised and the best known is inequality isoperimétrica flat. They were later appeared numerous variants of this inequality and generalizations to higher dimensions, develop a large field of geometric inequalities comparing the value of different geometric quantities of a conjunto.En Alongside these disparities were emerging many inequities isoperimétricas on. They sought to compare the area (or volume in excess of two dimensions) of a set E on the perimeter, meaning it far side of the border E, in particular the part of the border that was included in another set G open (on border). Motivation of this thesis has been to extend the notion of inequality isoperimétrica on geometric relative inequality, which compares other geometric figures relating addition to the area and perimeter is considered relativo.Si G a set of open space euclideo and is a subdivision of G by a continuous curve into two subsets E and GE with vacuum and not internal border rectificable, defines the geometric inequalities relating comparing magnitudes as inequalities that provide information on E, not a absolutely, but in its relationship with all its complementary atmosphere Go GE.: C1 greater = m (E, G) / g (E, G) "greater = C2, where m (E, G) and g (E, G ) are geometric quantities relative and C1, C2 and are not constant negative. One objective of this thesis is to get the geometric constants related, which are defined as rnfimo and supreme reason given, as well as the sets for those who these levels are reached, called maximizadores and minimizadores. will also be explored characteristics and properties of geometric sets extremales. Inequalities geometric studied in this report compares the following sizes: 1) Diameters on (maximum and minimum) on the perimeter, 2) Inradios relative (maximum and minimum) on the perimeter, 3) Inequalities isodiámetricas on, which compares the relative size with diameters relative 4) Volume on the inradios relative 5) Volume relative widths relative and 6 ) Inequalities on geometric surfaces and convex compact, comparing the surface area on the perimeter and on the relative diameters. finally describes a number of applications of these inequities, both other branches of mathematics to real-life problems . Some of these applications are known inequalities isodiamétricas related and others are applications originares of inequalities studied.

Author: MANJARÍN ARCAS MÓNICA.
Year: 2005.
University: AUTÓNOMA DE BARCELONA.
Place of defense: DEPARTAMENT DE MATEMÀTIQUES.
Place of preparation: DEPARTAMENT DE MATEMÁTIQUES.

Summary: Introducing and studied three procedures type varieties to build complex geometrical compacted through products, suspensions and bundles by leading circles from a class T-odd varieties of compact dimensions. Likewise, there are criteria for determining when such varieties are kind KÃ ¤ hler. The interest of the matter lies in the lack of results and examples Manageable compact complex varieties other than KÃ ¤ hler. The varieties of line are equipped with a structure almost normal contact, which is a vector field without zeros, a structure of CR maximum dimension and a transverse distribution to the field, all of them certain conditions to verify compatibility. In the first part of the tesi discusses examples of this type of varieties and producing a new family structures almost normal contact groups compact Lie related semisimples that unlike the known so far are not invariant to the left. The second part discusses three procedures for defining complex structures on certain varieties obtained from compact varieties dela class T. The third part demonstrate criteria for deciding which of the complex varieties obtained admit metrics KÃ ¤ hler. We tested that there is an obstruction to the complex varieties can obtain a metric KÃ ¤ hler: class cohomología defined from the normal structure almost touch, it should be annual. When varieties of departure check a hypothesis further, more precisely, when the vector field Killing is a partner, we can provide a necessary and sufficient criteria in two of the buildings. In the third construction demonstrate caracterizaicón complete in some cases. Finally we discuss examples dimension complex 2.