VARIATIONAL PROBLEMS FOR INTEGRAL INVARIANTS OF THE SECOND FUNDAMENTAL FORM OF A MAP BETWEEN PSEUDO-RIEMANNIAN MANIFOLDS

Akiyama, Rika; Sakai, Takashi; Sato, Yuichiro

doi:https://doi.org/10.18910/93064

VARIATIONAL PROBLEMS FOR INTEGRAL INVARIANTS OF THE SECOND FUNDAMENTAL FORM OF A MAP BETWEEN PSEUDO-RIEMANNIAN MANIFOLDS

Akiyama, Rika; Sakai, Takashi; Sato, Yuichiro

Osaka Journal of Mathematics, 2023, 60(4), 873-901

アクセス数:355件（2026-07-16 08:08 集計）

固定URL: https://doi.org/10.18910/93064

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タイトル	VARIATIONAL PROBLEMS FOR INTEGRAL INVARIANTS OF THE SECOND FUNDAMENTAL FORM OF A MAP BETWEEN PSEUDO-RIEMANNIAN MANIFOLDS
著者	著者名 Akiyama, Rika
	NRID 1000030381445 1000030381445 著者名 Sakai, Takashi
	著者名 Sato, Yuichiro
抄録	We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae for integral invariants defined from invariant homogeneous polynomials of degree two. Among these integral invariants, we show that the Euler–Lagrange equation of the Chern–Federer energy functional is reduced to a second order PDE. Then we give some examples of Chern–Federer submanifolds in Riemannian space forms.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	60(4)
ページ	873-901
刊行年月	2023-10
言語	英語
ハンドルURL	https://hdl.handle.net/11094/93064
DOI	https://doi.org/10.18910/93064
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 60, Number 4 （2023-10）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2023, 60(4), p. 873-901
DC.title	VARIATIONAL PROBLEMS FOR INTEGRAL INVARIANTS OF THE SECOND FUNDAMENTAL FORM OF A MAP BETWEEN PSEUDO-RIEMANNIAN MANIFOLDS
DC.creator	Akiyama, Rika
	Sakai, Takashi
	Sato, Yuichiro
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2023-10
DCTERMS.abstract	We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae for integral invariants defined from invariant homogeneous polynomials of degree two. Among these integral invariants, we show that the Euler–Lagrange equation of the Chern–Federer energy functional is reduced to a second order PDE. Then we give some examples of Chern–Federer submanifolds in Riemannian space forms.
DC.identifier	10.18910/93064
DC.format	93064
citation_title	VARIATIONAL PROBLEMS FOR INTEGRAL INVARIANTS OF THE SECOND FUNDAMENTAL FORM OF A MAP BETWEEN PSEUDO-RIEMANNIAN MANIFOLDS
citation_author	Akiyama, Rika
	Sakai, Takashi
	Sato, Yuichiro
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2023-10
citation_journal_title	Osaka Journal of Mathematics
citation_volume	60
citation_issue	4
citation_firstpage	873
citation_lastpage	901
citation_public_url	https://hdl.handle.net/11094/93064
citation_doi_detail	10.18910/93064
citation_doi	https://doi.org/10.18910/93064

VARIATIONAL PROBLEMS FOR INTEGRAL INVARIANTS OF THE SECOND FUNDAMENTAL FORM OF A MAP BETWEEN PSEUDO-RIEMANNIAN MANIFOLDS

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