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Development of geometric shage generation theory based on integrable discrete differential geometry associated with large group and discrete geometric analysis
About This Project
- Japan Grant Number
- JP25K21661 (JGN)
- Funding Program
- Grants-in-Aid for Scientific Research
- Funding Organization
- Japan Society for the Promotion of Science
Kakenhi Information
- Project/Area Number
- 25K21661
- Research Category
- Grant-in-Aid for Challenging Research (Pioneering)
- Allocation Type
-
- Multi-year Fund
- Review Section / Research Field
-
- Medium-sized Section 12:Analysis, applied mathematics, and related fields
- Research Institution
-
- Kyushu University
- Project Period (FY)
- 2025-06-27 〜 2030-03-31
- Project Status
- Granted
- Budget Amount*help
- 25,610,000 Yen (Direct Cost: 19,700,000 Yen Indirect Cost: 5,910,000 Yen)
Research Abstract
建築や工業意匠設計を視野に，美的性と力学的合理性を有し，施工性に優れた形状を幾何学で統制しつつ生成する数学基盤「幾何学的形状生成理論」を開拓する．そのために大きな群の幾何学と可積分性，対称性に基づく「美的形状の幾何学」，力学的特性と形状を可積分離散曲面論で同時に統制する離散曲面論を展開し，群作用に関する不変量の観点を導入して柔軟な形状生成手法を構築する．また，離散幾何解析の手法を取り込み，グラフに付随する曲率を用いて離散曲面構造の安定性を測る指標と，グラフラプラシアンのスペクトルから動的な振動モードの解析手法を構築し，曲面構造変形の遷移点の予測と安全性評価に対する新しい数学的手法を開拓する．
Details 詳細情報について
-
- CRID
- 1040867731180799616
-
- Text Lang
- ja
-
- Data Source
-
- KAKEN