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On<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math>-Symmetric<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>N</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Paracontact Metric Manifolds
The notions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math>-symmetric, 3-dimensional locally<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math>-symmetric,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math>-Ricci symmetric, and 3-dimensional locally<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math>-Ricci symmetric<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mi>N</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-paracontact metric manifolds have been introduced and properties of these structures have been discussed.