Yaermaimaiti Tuerxunmaimaiti,Division of Mathematics and Mathematical Science, Nagoya Institute of
Technology, Nagoya 466-8555, Japan; e-mail: yarimamat@gmail.com

Toshiaki Adachi,Department of Mathematics, Nagoya Institute of Technology, Nagoya 466-8555, Japan; e-mail: adachi@nitech.ac.jp

Abstract/Résumé:

We consider \((p,q)\)-step adjacency on a Kähler graph which is compounded from a principal graph and an auxiliary graph. We attach probabilistic weights to \((p,q)\)-step paths so that these paths show trajectories under the influence of a magnetic field of strength \(q/p\) on this graph. We study eigenvalues of Laplacians corresponding to \((p,q)\)-step paths on some regular Kähler graphs and give examples of pairs of regular Kähler graphs whose Laplacians for arbitrary pairs \((p,q)\) of positive integers have the same eigenvalues.

On considère la relation de contiguité à un pas \((p,q)\) près sur un graphe kählerien qui se constitue d’un graphe principal et un graphe auxiliaire. On attache des poids probabilistiques aux sentiers dans un tel graphe composés de pas \((p,q)\) de sorte que ces sentiers montrent des trajectoires sous l’influence d’un champs magnétique de force \(q/p\) sur le graphe. On étudie le spectre de l’opérateur laplacien correspondant aux sentiers aux pas \((p,q)\) sur certains graphes kähleriens regulières. On donne un example de deux graphes différents dont les opérateurs laplaciens ont le même spectre pour toute paire \((p,q)\).

Keywords: (p; q)-Laplacians, Kähler graphs, complement graphs, derived graphs, isospectral, products of graphs

AMS Subject Classification: Graphs and matrices, Hermitian and K_õhlerian manifolds 05C50, 53C55

PDF(click to download): Laplacians for Derived Graphs of Regular Kähler Graphs

T. Oguro

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Almost Kähler manifolds, Kahler manifolds, Symmetric spaces

AMS Subject Classification: Special Riemannian manifolds (Einstein; Sasakian; etc.), Symmetric spaces, Hermitian and K_õhlerian manifolds 53C25, 53C35, 53C55

PDF(click to download): Examples of non-Kähler, almost Kähler symmetric spaces

X. Liu

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Kaehler surface, quaternion projective space, signature

AMS Subject Classification: Global submanifolds, Hermitian and K_õhlerian manifolds 53C40, 53C55

PDF(click to download): The signature of Kaehler surfaces immersed into HPn(l)

D. Perrone

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Hopf surfaces, Isospectral problem, Spectrum of the Laplacian, generalized Hopf manifolds

AMS Subject Classification: Hermitian and K_õhlerian manifolds, 53C55, 58G25

PDF(click to download): Spectral rigidity of Hopf surfaces