String theorists are interested in several quantum field theories and string theories associated with Calabi–Yau threefolds. The most straightforward of these to formulate is the two-dimensional quantum field theory which governs the physics of a string propagating on the Calabi–Yau threefold. However, making calculations directly with that quantum field theory is quite difficult. To the extent...

It has recently been realized that a large class of Calabi-Yau models in which the VEV of the gauge connection is not set equal to the spin connection of the Calabi-Yau manifold are valid classical solutions of string theory. We provide some examples of three generation models based on such generalized Calabi-Yau compactifications, including models with observable gauge group SU (3) × SU (2) × ...

In this paper we investigate the spectral problem in Finsler geometry. Due to nonlinearity of Finsler–Laplacian operator, introduce faithful dimension pairs by means which spectrum a compact reversible metric measure manifold is defined. Various upper and lower bounds such eigenvalues are provided spirit Cheng, Buser Gromov, extend several aspects results Hassannezhad, Kokarev Polterovich. More...

Department of Obstetrics and Gynecology, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan Department of Obstetrics and Gynecology, Kuo General Hospital, Tainan, Taiwan Department of Pediatrics, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan *Correspondence to: Pao-Lin Kuo. E...

A Calabi–Yau manifold is a compact Kähler manifold with trivial canonical class such that the intermediate cohomologies of its structure sheaf are all trivial (h(X,OX ) = 0 for 0 < i < dim(X)). One handy way of constructing Calabi–Yau manifolds is by taking coverings of some smooth varieties such that some multiples of their anticanonical class have global sections. Indeed many of known example...

Of late there has been a great deal of interest in special Lagrangian submanifolds and manifolds fibred in special Lagrangian submanifolds, motivated by the Strominger-Yau-Zaslow conjecture [29]. One of the basic approaches to finding examples is to exploit symmetries of the ambient manifold. If X is a (non-compact) n-dimensional Calabi-Yau manifold with Kähler form ω and nowhere vanishing holo...

2009 Introduction In the following we describe some examples of Calabi-Yau manifolds that arise as desingularizations of certain Siegel threefolds. Here by a Calabi-Yau mani-fold we understand a smooth complex projective variety which admits a holo-morphic differential form of degree three without zeros and such that the first Betti number is zero. This differential form is unique up to a const...

a Department of Early Childhood and Family Education, College of Education, National Taipei University of Education, Taiwan b Department of Public Health, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Taiwan c Department of Pediatrics, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Taiwan d Department...