@article{article_339323, title={Some Symmetry Properties of Almost S-Manifolds}, journal={Celal Bayar University Journal of Science}, volume={13}, pages={657–664}, year={2017}, DOI={10.18466/cbayarfbe.339323}, author={Balkan, Yavuz Selim and Sarikaya, Mehmet Zeki}, keywords={-Einstein Manifold,-Ricci Symmetric Manifolds,Almost -Manifold,Globally Framed Metric -Manifold,-Structure,Weakly Symmetric Manifold}, abstract={<p style="text-align: justify; "> <span style="font-size: 10pt; font-family: "Times New Roman", serif;">Manifold theory is an important topic in differential geometry. Riemannian manifolds are a wide class of differentiable manifolds.  Riemannian manifolds consist of two fundamental class, as contact manifolds and complex manifolds. The notion of globally framed metric </span> <span lang="EN-US" style="font-size: 10pt; font-family: "Times New Roman", serif;"> <span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"> <v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"> <o:lock v:ext="edit" aspectratio="t"> </o:lock> </v:path> </v:stroke> </v:shapetype> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:12pt; height:16.5pt" o:ole=""> <v:imagedata src="file:///F:\Users\MUSTAF~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.wmz" o:title=""> </v:imagedata> </v:shape> </span> <!--[if gte mso 9]> <xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1567537665"> </o:OLEObject> </xml> <![endif]-->-manifold is a generalization of these fundamental classes. Almost <span style="position:relative;top:3.0pt;mso-text-raise:-3.0pt"> <v:shape id="_x0000_i1026" type="#_x0000_t75" style="width:11.25pt;height:14.25pt" o:ole=""> <v:imagedata src="file:///F:\Users\MUSTAF~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz" o:title=""> </v:imagedata> </v:shape> </span> <!--[if gte mso 9]> <xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1567537666"> </o:OLEObject> </xml> <![endif]-->-manifolds which are globally framed metric <span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"> <v:shape id="_x0000_i1027" type="#_x0000_t75" style="width:12pt;height:16.5pt" o:ole=""> <v:imagedata src="file:///F:\Users\MUSTAF~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.wmz" o:title=""> </v:imagedata> </v:shape> </span> <!--[if gte mso 9]> <xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1567537667"> </o:OLEObject> </xml> <![endif]-->-manifold generalize some contact manifolds carrying their dimension to <span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"> <v:shape id="_x0000_i1028" type="#_x0000_t75" style="width:41.25pt;height:17.25pt" o:ole=""> <v:imagedata src="file:///F:\Users\MUSTAF~1\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz" o:title=""> </v:imagedata> </v:shape> </span> <!--[if gte mso 9]> <xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1567537668"> </o:OLEObject> </xml> <![endif]-->. On the other hand, classification is important for Riemannian manifolds with respect to some intrinsic and extrinsic tools as well as all sciences. Moreover, </span> <span lang="EN-US" style="font-size:10.0pt; font-family:"Times New Roman","serif";mso-fareast-font-family:"Times New Roman"; mso-font-kerning:8.0pt;mso-ansi-language:EN-US;mso-fareast-language:EN-US; mso-bidi-language:AR-SA">symmetric manifolds play an important role in differential geometry. There are a lot of symmetry type for Riemannian manifolds with respect to different arguments. </span> <span lang="EN-US" style="font-size: 10pt; font-family: "Times New Roman", serif;"> </span> <span style="font-size: 10pt; font-family: "Times New Roman", serif;">Under these considerations, in the present paper  we study some symmetry conditions on almost </span> <span lang="EN-US" style="font-size: 10pt; font-family: "Times New Roman", serif;"> <span style="position:relative;top:3.0pt; mso-text-raise:-3.0pt"> <v:shape id="_x0000_i1029" type="#_x0000_t75" style="width:11.25pt; height:14.25pt" o:ole=""> <v:imagedata src="file:///F:\Users\MUSTAF~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz" o:title=""> </v:imagedata> </v:shape> </span> <!--[if gte mso 9]> <xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1567537669"> </o:OLEObject> </xml> <![endif]-->-manifolds </span> <span style="font-size: 10pt; font-family: "Times New Roman", serif;">. We investigat}, number={3}, publisher={Manisa Celal Bayar University}