Search results for "differential geometry"
showing 10 items of 462 documents
From the theory of “congeneric surd equations” to “Segre's bicomplex numbers”
2015
We will study the historical pathway of the emergence of Tessarines or Bicomplex numbers, from their origin as "imaginary" solutions of irrational equations, to their insertion in the context of study of the algebras of hypercomplex numbers.
On Hodge theory for the generalized geometry (I)
2013
Abstract We first investigate the linear Dirac structure from the viewpoint of a mixed Hodge structure. Then we discuss a Hodge-decomposition-type theorem for the generalized Kahler manifold and study the moduli space of a generalized weak Calabi–Yau manifold. We present a holomorphic anomaly equation and a one-loop partition function in a topological B-model under the generalized geometric context.
Review of Some Development of the Hole Drilling Method
1990
This paper contains a survey of some developments of the hole drilling method. It is mainly based on the research work carried out at the University of Palermo in the years from 1978 to 1989. The paper considers the relationship between the relaxed strain and the residual stresses for a rosette with an off-centre hole, the influence of hole eccentricity on the determination of residual stresses and of rosette calibration constants, the sensitivity of strain relaxation.
THE HOROSPHERICAL GEOMETRY OF SUBMANIFOLDS IN HYPERBOLIC SPACE
2005
Some geometrical properties associated to the contact of submanifolds with hyperhorospheres in hyperbolic -space are studied as an application of the theory of Legendrian singularities.
Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds
2022
In this article we study the linearized anisotropic Calderon problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderon problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial ingredients in the proof of our result are the construction of Gaussian beam quasimodes on the tra…
Optimal control and Clairaut-Liouville metrics with applications
2014
The work of this thesis is about the study of the conjugate and cut loci of 2D riemannian or almost-riemannian metrics. We take the point of view of optimal control to apply the Pontryagin Maximum Principle in the purpose of characterize the extremals of the problem considered.We use geometric, numerical and integrability methods to study some Liouville and Clairaut-Liouville metrics on the sphere. In the degenerate case of revolution, the study of the ellipsoid uses geometric methods to fix the cut locus and the nature of the conjugate locus in the oblate and prolate cases. In the general case, extremals will have two distinct type of comportment which correspond to those observed in the r…
On the K-stability of complete intersections in polarized manifolds
2011
We consider the problem of existence of constant scalar curvature Kaehler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the ambient manifold. As applications we give a new Mukai-Umemura-Tian like example of Fano 5-fold admitting no Kaehler-Einstein metric and a strong evidence of K-stability of complete intersections on Grassmannians.
Applying differential geometric LARS algorithm to ultra-high dimensional feature space
2009
Variable selection is fundamental in high-dimensional statistical modeling. Many techniques to select relevant variables in generalized linear models are based on a penalized likelihood approach. In a recent paper, Fan and Lv (2008) proposed a sure independent screening (SIS) method to select relevant variables in a linear regression model defined on a ultrahigh dimensional feature space. Aim of this paper is to define a generalization of the SIS method for generalized linear models based on a differential geometric approach.
Generalizing LARS algorithm using differential geometry
2009
We propose a path following algorithm for generalized linear models that can be considered a differential geometric generalization of the LARS algorithm. In our approach we use differential geometry to generalize the equiangular condition on which is based the LARS algorithm and then we use a predictor-corrector method to compute the solution path of the coefficients.
De Rham–Hodge–Kodaira Operator on Loop Groups
1997
AbstractWe consider a based loop group Le(G) over a compact Lie groupG, endowed with its pinned Wiener measureν(the law of the Brownian bridge onG) and we shall calculate the Ricci curvature for differentialn-forms over Le(G). A type of Bochner–Weitzenböck formula for general differentialn-forms (or Shigekawa identity) will be established.