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Study on the general adiabatic expansion theory for Laplacian and its some applications

Research Project

Project/Area Number 23540070
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionSaitama University

Principal Investigator

NAGASE Masayoshi  埼玉大学, 理工学研究科, 教授 (30175509)

Co-Investigator(Renkei-kenkyūsha) MIZUTANI Tadayoshi  埼玉大学, 名誉教授 (20080492)
SAKAMOTO Kunio  埼玉大学, 大学院・理工学研究科, 教授 (70089829)
SHIMOKAWA Koya  埼玉大学, 大学院・理工学研究科, 教授 (60312633)
EGASHIRA Shinji  埼玉大学, 大学院・理工学研究科, 助教 (00261876)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsラプラシアン / 熱核 / 断熱展開 / 接触リーマン多様体 / 山辺問題 / Laplacian / asymptotic expansion / adiabatic expansion
Research Abstract

We clarified the usefulness and powerfulness of the general adiabatic expansion theory in studying some subjects related to Laplacian. In particular, based on the theory we obtained a formula for the coefficients of the asymptotic expansion of every derivative of the heat kernel associated to the Kohn-Rossi Laplacian on contact Riemannian manifold. In order to describe the coefficients explicitly up to an arbitrarily high order as universal polynomials built from the curvature, the torsion (of hermitian Tanno connection) and the Nijenhuis tensor, we need only a basic knowledge of calculus added to the formula. (The conventional method requires various kinds of profound knowledge and there may be few investigations on the coefficients.) We found also that the theory is useful for investigating the so-called CR-Yamabe problem.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (3 results)

All 2013 2012

All Journal Article (3 results) (of which Peer Reviewed: 3 results)

  • [Journal Article] On the trace and the infinitesimally deformed chiral anomaly of Dirac operators on twistor spaces and the change of metrics on the base spaces2013

    • Author(s)
      長瀬正義
    • Journal Title

      Saitama Math. J

      Volume: Vol.30 Pages: 39-57

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the trace and the infinitesimally deformed chiral anomaly of Dirac operators on twistor spaces and the change of metrics on the base spaces2013

    • Author(s)
      Masayoshi Nagase
    • Journal Title

      Saitama Math. J.

      Volume: 30 Pages: 39-57

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rational tangle surgery and Xer recombination on catenanes2012

    • Author(s)
      下川航也, 他
    • Journal Title

      Algebr. Geom. Topol

      Volume: Vol.12 Pages: 1183-1210

    • Related Report
      2013 Final Research Report
    • Peer Reviewed

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Published: 2011-08-05   Modified: 2019-07-29  

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