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Stationary‐Angle Conditions and Bertrand Offsets in Timelike‐Ruled Surfaces

ملخص البحث

In thisstudy,weintroducetheconceptofstationary-angletimelike-ruledsurfacesandexaminetheirgeometricproperties,
particularly inrelationtotheirBertrandoffsets.Atimelike-ruledsurfaceisgeneratedbythemotionofastraightrulingalonga
striction curve,anditsstructureisanalyzedusingtheBlaschkeandDarbouxframes.Wederivekeygeometricinvariants,including
spherical curvature,geodesiccurvature,normalcurvature,andgeodesictorsion.Additionally,weestablishtheconditionsunder
which thestrictioncurveofatimelike-ruledsurfacebehavesasageodesic,anasymptoticcurve,oracurvatureline.Specialcases,
such astimelike-tangentialdevelopablesandtimelike-cones,arealsodiscussed.Usingcurvature-axisanalysis,wedevelopahigher-
order contactframeworktobetterunderstandthebehaviorofthesesurfaces.Finally,weinvestigatetheBertrandoffsetsof
stationary-angle timelike-ruledsurfaces,provingthattheypreserveastationaryanglebetweentheirrulingsanddetermining
the necessaryconditionsfortheirexistence.ThisworkenhancestheunderstandingofdifferentialgeometryinLorentzianspaces
and providesnewinsightsintoruledsurfacesinMinkowskispace.

مؤلف البحث
Rashad A. Abdel-Baky
تاريخ البحث
قسم البحث
مجلة البحث
Advances in Mathematical Physics
سنة البحث
2025