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They are the desired generalization on Finsler manifolds of the corresponding Gromoll-Meyer's splitting lemmas on Riemannian manifolds (\\cite{GM1, GM2}). As an application we extend to Finsler manifolds a result by Grove and Tanaka \\cite{GroTa78, Tan82} about the existence of infinitely many, geometrically distinct, isometry invariant clos"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.3209","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-12T15:45:07Z","cross_cats_sorted":["math.DS","math.GT"],"title_canon_sha256":"650c2c48edb636c6565f9a167cc3835b6ca2da5ecd84f87b9b1c6544a6314bb3","abstract_canon_sha256":"3532d03c231f42c8e7fce84ce00473451fb4095ea2c7ccb62f478cc29905e88a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:38.899146Z","signature_b64":"etV5DICk05kU4Em8Qfbq/dPABSfDzgdMOZ3NE3t57sFyAG9fftGKRzLImraauwPp6X9FVoO7c7rJ4OtKX9iWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9864679cd88714288328a65502dbc2bed231bf19d22532aa4a537d08f2f26fb","last_reissued_at":"2026-05-18T01:15:38.898545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:38.898545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Splitting lemmas for the Finsler energy functional on the space of $H^1$-curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.DG","authors_text":"Guangcun Lu","submitted_at":"2014-11-12T15:45:07Z","abstract_excerpt":"We establish the splitting lemmas (or generalized Morse lemmas) for the energy functionals of Finsler metrics on the natural Hilbert manifolds of $H^1$-curves around a critical point or a critical $\\R^1$ orbit of a Finsler isometry invariant closed geodesic. 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